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Working Paver 9211
DYNAMICS OF THE TRADE BALANCE AND
THE TERMS OF TRADE: THE S-CURVE
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 fo'r financial
support. They also thank Fabio Canova, Michael
Gavin, Tiff Macklem, Patricia Reynolds, and
participants at the University of Rochester
Workshop, "International Transmission of
Business Cycles," for helpful comments on
earlier versions of this paper.
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.
October 1992

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ABSTRACT
We provide a theoretical interpretation of two features of international
data: t h e countercyclical movements in net exports and t h e tendency f o r the
t r a d e balance t o be negatively correlated with current and f u t u r e movements
in t h e t e r m s of trade, but positively correlated with past movements.
We
document these same properties in a two-country stochastic growth model in
which t r a d e fluctuations reflect, in large part, the dynamics of capital
formation.
We find t h a t the general equilibrium perspective i s essential:
The relation between t h e trade balance and the terms of t r a d e depends
critically on the source of fluctuations.

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We document some of the properties of short-term

fluctuations in the

t r a d e balance and the terms of trade in 11 OECD countries and interpret them
The terms of

from the perspective of a two-country stochastic growth model.
trade,

in this paper, is the relative price of imports t o exports and the

t r a d e balance i s the ratio of net exports t o output.
balance

is

uniformly

countercyclical

and,

is

negatively

correlated with current and f u t u r e movements in the terms of

trade, but

positively correlated with past movements.
t h e cross-correlation
S-curve,

in

We find t h a t the trade
general,

We call this asymmetric shape of

function f o r net exports and the terms of t r a d e the

since i t looks like a horizontal S.

This finding i s reminiscent of

earlier work on the J-curve (Junz and Rhomberg 1973, Magee 1973, and Meade
1988).
Our objective is t o provide a dynamic general equilibrium interpretation
of these properties.

The theoretical structure extends earlier work on trade

and price dynamics by Hodrick (1988) and Stockman and Svensson (19871, who
develop simple general equilibrium models in which both the t r a d e balance and
t h e terms of trade a r e endogenous.
imperfectly
arise

from

purchases.

substitutable
persistent

goods
shocks

In our economy, two countries produce

with
to

capital

aggregate

and

labor,

and

fluctuations

productivity

and

government

We find t h a t with plausible parameter values, t h i s theoretical

economy generates both countercyclical trade and an S-curve.

The dynamic

responses t o productivity shocks suggest a straightforward explanation f o r
both

properties.

A

favorable

domestic

productivity

shock

leads

to

an

increase in domestic output, a decrease in i t s relative price, and a rise in
t h e terms of trade.

Because the productivity shock is persistent, we also

s e e a rise in consumption and a temporary boom in investment, a s capital i s
shifted t o i t s most productive location.

The increases in consumption and

investment together a r e greater than the gain in output, and the economy

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experiences a t r a d e deficit during this period of high output.

This dynamic

response pattern gives r i s e t o countercyclical movements in t h e balance of
t r a d e and an asymmetric cross-correlation function much like t h e ones seen in
t h e data.
Investment dynamics play a central role in generating these properties
of our theoretical economy.

If we eliminate capital, t h e t r a d e balance is

simply a reflection of output dynamics and consumption smoothing.

Consider,

once more, t h e dynamic responses t o a domestic productivity shock.

In this

economy, preference f o r smooth consumption results in a smaller increase in
consumption than in output and an improvement in the balance of trade.

Thus,

the t r a d e balance i s procyclical r a t h e r than countercyclical, as i t is in t h e
economy with capital.

At the same time, the price of domestic goods f a l l s

and the terms of t r a d e rises.

Since the shocks (and hence the fluctuations

in t r a d e and prices) a r e persistent,
cross-correlation function:

the economy generates a tent-shaped

The asymmetric pattern we call t h e S-curve does

not arise when the economy has no capital.
We find t h a t the general equilibrium perspective i s essential,
sense

that

the

correlations

critically on t h e source of

between

trade

fluctuations.

and

relative

in the

prices

depend

Although t h i s implication of t h e

theory is, in some ways, obvious, i t differs sharply from t h e large body of
work

in

international

macroeconomics

based

on

the

small

assumption, in which relative price movements a r e exogenous.
source of

open

economy

Because the

relative price movements i s not specified in these models,

the

relation between trade and prices is independent of them by assumption.

In

our general equilibrium setting, the source is critical.

We illustrate t h i s

feature of the theory in an economy with shocks t o government spending rather
than

productivity.

In

this

case,

the

cross-correlation

function f o r

exports and the terms of trade i s tent-shaped, rather than S-shaped.

net
The

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difference

between

cross-correlation

functions

with

shocks

to

productivity

and government spending makes i t clear t h a t there i s no simple structural
relation, in our economy, between the t r a d e balance and t h e terms of t r a d e
and suggests t h a t one cannot characterize the relation between t r a d e and
prices without specifying t h e source of their fluctuations.
These points a r e developed in the r e s t of

I,

Section

with

a

description

of

postwar

the paper.

quarterly

We s t a r t , in

data,

including

the

cyclical behavior of net exports and the correlations between net exports and
In Section 11, we describe a

t h e t e r m s of trade, f o r 11 developed countries.
theoretical economy with two countries t h a t
capital

and

purchases.

labor

and

that

face

shocks

produce different goods with

to

productivity

and

government

In Section 111, we discuss the selection of parameter values and

our method of computing equilibrium time paths f o r net exports, the terms of
trade,

and

other

variables.

In

Section

IV,

we

turn

to

the

model's

properties, including the correlation between net exports and the terms of
trade.
capital

Section V i s devoted t o two extreme experiments:
and

investment,

and

with

shocks

to

the economy without

government

spending

Section VI is devoted t o some additional features of the theory,

alone.

including

two t h a t we term anomalies: properties f o r which there remains a substantial
difference between theory and data.
usefulness of

our

theoretical

We conclude with a few remarks on t h e

framework f o r

interpreting t r a d e and price

movements and other features of international time series data.

I.

P r o p e r t i e s of t h e Data
We

developed

start

by

countries.

looking
The

at

postwar

data

Cooperation and Development's

are

quarterly

from the

trade

statistics

Organization

for

for

11

Economic

(OECD's) Quarterly National Accounts and a r e

described more completely in the Appendix.

W e measure t h e t r a d e balance,

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labeled nx, a s t h e r a t i o of net exports t o output, with both measured in
current prices as reported in national income and product accounts.

The

terms of trade, labeled p, i s t h e r a t i o of t h e implicit price deflators f o r
imports and exports

--

the relative price of imported goods.

either GNP o r GDP in constant prices, and i s labeled y.
p and y r e f e r

to

logarithms

of

those

variables.

Real output i s

Statistics f o r both

Throughout the

paper,

properties of both international time series d a t a and theoretical economies
r e f e r t o Hodrick-Prescott

filtered variables.

The properties of t h i s f i l t e r

a r e described in some detail by Hassler e t al. (1992) and King and Rebelo
(1989).

We

simply

note

that

the

filter

leaves

us

with

short-term

fluctuations in t h e variables being studied.
In Table 1, we report some of the salient properties of fluctuations in
t h e t r a d e balance and t h e terms of trade.

W e list, f i r s t , the standard

deviations of net exports, the terms of trade, and output.

A f a i r amount of

heterogeneity exists across countries in the magnitudes of these statistics,
particularly in t h e t r a d e variables.

The standard deviation of the r a t i o of

net exports t o output ranges from a low of 0.45 percent f o r the United S t a t e s
t o a high of 1.75 f o r Finland.
percent.

The median value, in our sample, i s 1.06

The standard deviation of the terms of t r a d e varies somewhat more,

from 1.63 in Austria t o 5.86 in Japan.
Second,
persistent.

both

t h e trade balance and the terms of

t r a d e a r e highly

The autocorrelation of net exports extends from 0.29 in Austria

t o 0.90 in Switzerland, with a median of 0.71.

The autocorrelation of the

terms of t r a d e ranges from 0.50 f o r Austria t o 0.88 in Japan and Switzerland,
with a median of 0.80.
Third, net exports a r e countercyclical in every country in our sample.
This f e a t u r e has been noted elsewhere by Blackburn and Ravn (1991) and
Danthine and Donaldson (1991). among others, and i s implicit in t h e strong

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relations between imports and income in most macroeconometric models.
Fourth,

t h e contemporaneous correlation

between

net

exports and the

terms of t r a d e varies somewhat across countries, but i s negative more often
than not.

In Finland, France,

Italy,

Japan,

Kingdom, the correlations a r e less than -0.4.

Switzerland,

and the United

The United S t a t e s i s the only

country in our sample f o r which these two variables have a sizable positive
contemporaneous correlation.

Mendoza (1990) provides evidence f o r additional

countries a t an annual frequency.
The contemporaneous correlations between net exports and t h e terms of
t r a d e ignore, however, the complex dynamic relation between these variables
suggested by earlier work.

In Figure 1, we graph cross-correlation functions

for

for

these

two

variables,

leads

and

lags

up

to

two

years:

f o r k between -8 and 8.
correlations, t h a t is, between pt and nx
t+k

the
This

function i s typically negative f o r negative values of k (the left side of t h e
horizontal axis), but t u r n s positive f o r k between 2 and 4.

This general

pattern, moreover, does not seem t o be the result of the sample periods used.
In Figure 2, we report cross-correlation functions f o r t h e periods before and
a f t e r 1972 f o r the f o u r countries f o r which we have d a t a going back t o 1955.
Japan and the United Kingdom exhibit the same shape in both the Bretton Woods
period (1955-71) and the more recent floating-rate period (1972-90).
shows little relation between the two variables,
either period.

Canada

at any lead o r lag, f o r

For the United States, the cross-correlation function f o r the

earlier period i s similar t o t h a t of Japan and the United Kingdom, as well as
8 of the 11 countries in Figure 1.

The United S t a t e s in this period differs

slightly from these other countries in t h a t the function crosses the axis t o
the left of k=O, r a t h e r than the right, but the shape i s otherwise similar.
The United

States in

different pattern.

the l a t t e r period,

however,

displays a substantially

If we further divide the post-1972 period into the 1970s

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and 1980s, we find (not reported) t h a t this change in U.S. t r a d e and price
performance applies t o both decades:
cross-correlation

In neither decade i s t h e shape of the

like t h a t of the Bretton Woods period in the United States,

the United Kingdom, and Japan in both subperiods, o r in 8 of the 11 countries
of Figure 1.
We label the characteristic asymmetric shape of
function f o r

net

exports and

the terms

of

trade

the cross-correlation
the

S-curve,

since

it

resembles a horizontal S, but readers may notice a resemblance t o the J-curve
of earlier work.

In studies of devaluations, i t was frequently noted t h a t

unfavorable movements in the terms of trade (increases, in our terminology)
were generally associated with declines in the balance of t r a d e t h a t reversed
themselves 6 t o 24 months
J-curve.
Artus

later.

This pattern was referred t o a s the

A classic example ' i s the 1967 sterling devaluation described by
(1975).

This property

of

devaluations spawned subsequent

studies,

including those cited by Junz and Rhomberg (19731, Magee (19731, and Meade
(19881, in which observed trade and price dynamics were attributed to, among
other things, lags between order and delivery of imported goods and the time
required f o r exporters t o change capacity.

We return t o these issues in

Section IV.
In short,

we find a

number

exports and the terms of trade:
balance

is

consistently

of

regularities

in the behavior

of

net

both a r e highly autocorrelated; the t r a d e

countercyclical;

and

the

cross-correlation

function

f o r net exports and the terms of trade has an asymmetrical shape we call the
S-curve.

11.

A Theoretical Economy
We

compare

these

properties

o f international

data

to

those

of

a

stochastic growth model with two countries, each inhabited by a large number

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of identical agents.
of

Kydland

produces

and

a

This world economy i s a streamlined two-country version

Prescott's

different

internationally

(1982) closed

good

immobile.

with

economy,

its

Fluctuations

own

in

which

technology

each

and

country

labor

is

a r e driven by stochastic shocks t o

productivity and government purchases of goods and services.
Preferences

of

the

representative

agent

in

each

country

i

are

characterized by utility functions of the form

where U(c.1-n) = 1c'(l-n1~"1'/~,

and cit and n

it

a r e consumption and hours

worked, respectively, in country i.
With

respect

to

the

technology,

each

country

specializes

in

the

production of a single good, labeled "a" f o r country 1 and "b" f o r country 2.
The

goods

are

produced

using

capital,

k,

and

labor,

homogeneous production functions of the same form.

n,

with

linear

This gives rise t o t h e

resource constraints,

8 1-8
in countries 1 and 2, respectively, with F(k,n) = k n
.

The quantity y

denotes GDP in country i, measured in units of the local good, and a
b.

lt

denote uses of the two goods in country i.

country 1 t o country 2, and blt

it

it

and

Thus a2t denotes exports from

represents imports into country 1.

The

vector z = (z , z 1 i s a stochastic shock t o productivity whose properties
t
It 2t
will be described shortly.
Consumption, investment, and government purchases
g, respectively

--

--

denoted c, x, and

a r e composites of foreign and domestic goods:

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-

where G(a,b) = [ula p+02b-pl-1/P
Hence,

i s homogeneous of degree one and ph-1.

a l l t h r e e final uses of goods and services have both foreign and

domestic

content,

and

in

the

same

proportions.

The

substitution between foreign and domestic goods i s cr=l/(l+p).

elasticity

of

This device

f o r aggregating domestic and foreign goods was suggested by Armington (1969)
and i s a standard f e a t u r e of general equilibrium t r a d e models (Whalley 1985,
Deardorff and Stern 1990).
aggregator.

Accordingly, we r e f e r t o G as an Armington

The weights oi in the aggregator function G allow us t o specify

the domestic and foreign content of domestic spending.

Government purchases,

g, a r e stochastic; we describe their behavior below.
Capital formation embodies the time-to-build
Prescott (1982).

structure of Kydland and

As in their economy, i t takes J quarters t o augment the

productive capital stock.

A unit increase in the capital stock J q u a r t e r s

from now involves purchases of 1/J units of the final good f o r J consecutive
quarters.

To express this mathematically, let sit be planned additions t o

the capital stock of country i in period t+J.

The capital stocks then evolve

according t o

where 6 i s the depreciation rate.

In period t , total expenditure on gross

capital formation i s

the sum of

capital expenditures on all currently active projects.

In all

experiments but one, we s e t J=1, s o investment expenditures made in period t

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increase t h e stock of capital in period t+l.
Finally, the underlying shocks t o our economy a r e independent bivariate
autoregressions.

Z

where c

The technology shocks follow

i s distributed normally and independently over time with variance

The correlation between the technology shocks, z and z
is determined
1
2'

VZ.

by the off-diagonal elements of A and V

Similarly, shocks t o government

z'

spending a r e governed by

where

g

t

=

( g ,g 1 and
It 2t

cg is

distributed

normally

with

variance

V

8'

Technology shocks, z, and government spending shocks, g, a r e independent.
From these

elements,

we

can construct national

income and

accounts f o r each country of our theoretical world economy.

GDP in country 1

a t d a t e t , in units of the domestically produced good, i s ylt;

components

as

follows.

The

the resource

We relate national output t o

constraint equates this t o the sum a +a
I t 2t'
expenditure

product

Armington

a s a function of a
and blt.
absorption, c +x +g
I t It It'
It

aggregator

expresses

Since t h e aggregator,

G, i s homogeneous of degree one, we have, in equilibrium,

where q

It

and q

2t

a r e the prices of the two goods a t date t.

Using t h e

resource constraint, we can express output a s

where p

t

absorption,

= qZt/qlt

i s the terms of

( c +x +g )/q
I t I t It
It'

trade.

and net exports,

Thus output is the sum of
a2t 'Pt

bit'

We measure t h e

t r a d e balance in the model just a s we do in the data, a s the ratio of net

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exports t o output, with both measured in current prices:
nx

--

t

(a2t-~tblt)/~lt'

We compute the terms of t r a d e in country 1 from

t h e marginal r a t e of

transformation

between the two goods in country

1,

evaluated a t equilibrium quantities.

111.

P a r a m e t e r Values, Steady S t a t e , a n d Computation
We

describe,

parameter

values,

equilibrium.
Prescott's

briefly,
listed

Both
(1982)

our
in

procedures

Table

2,

a r e adapted t o
closed

economy

and

the
study;

for

selecting

for

computing

open
for

economy

the

benchmark

a

competitive

from

details,

see

Kydland
their

and
paper

(Sections 4 and 5 ) and Backus, Kehoe, and Kydland (1992a, Sections I1 and
111).

A s a rule, share parameters f o r preferences and production a r e chosen

t o equate means of ratios of - aggregate U.S. time series t o analogous ratios
for

the

theoretical

economy's

steady

state.

selected' from existing statistical studies.
United

States

parameters of

and

an

aggregate

the technology

of

process,

Curvature

parameters

are

We use Solow residuals f o r the

European

countries

which result

to

estimate

in productivity

t h a t a r e highly persistent and positively correlated across countries.

the

shocks
The

only new elements a r e the parameters of the Armington aggregator and those
t h a t govern the behavior of shocks t o government spending, both of which we
describe below.
equilibrium by

Given values f o r the model's parameters,
solving numerically

a

quadratic

we compute an

approximation

to

a

social

planner's problem t h a t weights equally the utility of consumers in t h e two
countries.
The most important parameters in this paper a r e those of t h e Armington

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aggregator, which govern the elasticity of substitution between foreign and
domestic goods and the average r a t i o of imports t o output.

The elasticity of

substitution is cr=l/(l+p), and t h e r e is some uncertainty about what value of
this parameter

i s indicated by the data; see, f o r example, t h e survey of

estimates provided

by

Stern,

Francis,

and Schumacher

(1976).

The most

reliable studies seem t o indicate t h a t f o r the United States, t h e elasticity
i s between one and two, and values in this range a r e generally used in
empirical t r a d e models.
the

For Japan and an aggregate of European countries,

elasticity seems t o be

smaller;

see, f o r

example,

the

Deardorff and Stern (1990, ch. 3) and Whalley (1985, ch. 5).

1

and w

2

in

W e use cr=1.5 a s

our starting point, but experiment with other values a s well.

w

discussions

W e determine

from observed ratios of imports and exports t o GDP using the

f irst-order condition

In a symmetric steady s t a t e with y =y
b =a
and p=l, the r a t i o a /b can
1 1
1 2' 1 2'
be expressed a s (1-bl/yl)/(bl/yl),
in country 1.
of

w

where bl/yl

With p=l, this determines the ratio w /w
2 1'

and w so t h a t the steady-state
2

1

normalization.

i s the ratio of imports t o GDP

value of

y

1

We s e t the levels

i s one,

a convenient

We use an import share of 0.15, which i s slightly greater

than i t s average value in the United States, Japan, and Europe (in aggregate,
with

intra-European

discussion of

t r a d e excluded) over t h e

last

decade.

government spending shocks until they a r e used

We

postpone

in the next

section.
We

use

these

parameter

values

as

alternative values in the following sections.

a

benchmark,

but

also

consider

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IV. P r o p e r t i e s of t h e Theoretical Economy
We a r e now in a position t o compute equilibrium time paths f o r variables
in our theoretical economy and compare their properties t o those of

the

We do this f o r the benchmark parameter

aggregate d a t a we reviewed earlier.

values, described in the previous section and summarized in Table 2, and also
f o r some other values.

This analysis helps us to assess the role of various

parameters in generating specific properties of the theoretical economy and
gives us some feeling f o r the robustness

of

these properties.

It

also

provides some intuition f o r the model's behavior.
Our primary objective is t o document the theoretical relation between
net exports and the terms of trade and t o determine, in particular, whether
the theory can account f o r the asymmetric cross-correlation function f o r the
trade balance and the terms of trade

--

find i t useful

t o start,

with some summary statistics.

statistics shed

light

on

however,
aspects of

what we have called t h e S-curve.

the model t h a t

play

We
These

a role

in the

dynamics of net exports and the terms of trade, and may also have some
independent interest.

Thus we report, in Table 3, the same properties of the

theoretical economy that we documented f o r 11 OECD countries in Table 1.

The

f i r s t row, which we refer t o as the benchmark economy, uses the parameter
values specified in the last section and listed in Table 2.
We find, f i r s t , t h a t both net exports and the terms of t r a d e a r e highly
autocorrelated

in

our

theoretical

economy.

The

autocorrelation

of

net

exports is somewhat less than we see in the data (0.61 in t h e model v. a
median of 0.71 in the data), but i s within the range observed f o r other
countries.
very

The autocorrelation of the terms of trade in the model (0.83) is

close t o

i t s median

properties is surprising:

value

in the

data

The variables of

(0.80).

Neither

of

these

the model inherit t o a large

extent the high degree of persistence in the technology shocks.

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We turn next t o correlations between net exports and other variables.
In

the

benchmark

economy,

net

exports

are

countercyclical:

contemporaneous correlation with output i s -0.64.
stronger than we see in U.S.

data (-0.221,

but

This characteristic i s
i s within t h e range of

variation observed across t h e 11 countries of our sample (-0.17
There

is

a

countercyclical

sense

in

which

fluctuations

investment
in

net

is

essential

exports.

The

The

in

generating

trade

investment a r e connected, a s we know, by a n identity:

t o -0.68).
these

balance

and

Net exports i s the

difference, in our economy, between output and the sum of consumption and
investment a t market prices.

Consumers' desire f o r smooth consumption will

lead, a s seen in Section VI,

t o a standard deviation of consumption about

half that of output.
Countercyclical

As a result, output net of consumption is procyclical.

movements

in

the

procyclical movements in investment.

balance

of

trade

also

require

strong

In the model, a s in the data, these

fluctuations a r e large enough t o make absorption more variable than output
over the cycle and thus give rise t o a negative correlation between net
exports and output.
A third feature of the benchmark economy i s a strong inverse relation
between net exports and the terms of trade:

The t r a d e balance i s generally

positive when the relative price of foreign goods is low.

This correlation

i s generally

S t a t e s being a

negative in the data, too,

notable exception.

with

the United

We also find that the correlation between t h e terms of

t r a d e and output is strongly positive in the theoretical economy;

in t h e

data, there i s no obvious regularity.
With this background, we turn t o the cross-correlation function f o r net
exports and the terms of trade.

We see, in Figure 3, t h a t this function

takes the S-curve shape t h a t we documented f o r 8 of 11 countries in Figure 1.
Thus, the theory delivers one of the striking features of t h e data.

We can

clevelandfed.org/research/workpaper/index.cfm

get some intuition f o r the behavior underlying t h i s correlation from Figure
4, where we graph the dynamic responses of t h e terms of t r a d e and other
variables t o a one-time positive shock t o domestic productivity.

On impact,

we see a n increase in domestic output and thus a decrease in i t s relative
price, the inverse of the terms of trade.

In the second panel of the figure

we s e e t h a t this shock also raises consumption, but by less than half the
increase in output.

Investment,

on the other hand, grows by more than

consumption and t h e t r a d e balance moves initially into deficit.

As time

passes, the investment boom dissipates and the t r a d e deficit turns t o a
surplus.

This impulse response pattern gives rise, in the benchmark economy,

t o a negative contemporaneous correlation between net exports and the terms
of trade.

The correlation between pt and nx

t+k

increases with k in the

neighborhood of k=O, reflecting the positive slope of the dynamic response
function f o r net exports in Figure 4.

The reasoning behind the left side of

the cross-correlation function i s somewhat different.

To make this a s simple

a s possible, suppose the economy has only one shock and t h a t the t e r m s of
trade

is

Then

the

autoregressive

of

order

cross-correlation

geometrically a t r a t e a.

one,

function

with

autocorrelation

for

lags

kc0

coefficient

approaches

a.

zero

In the benchmark economy, t h e dynamics a r e slightly

more complex, and this example provides only an approximation t o the pattern
reported in Figure 3.
We see, then, t h a t the theory produces an S-curve and t h a t the dynamics
of net exports and t h e terms of t r a d e in our theoretical economy reflect, t o
a large extent, the influence of capital formation on t h e balance of trade.
We return t o this issue in the next section.
Table

3

particular

illustrate
parameters

government purchases.

the
and

sensitivity
the

of

influence

The remaining experiments of

these
on

properties
the

economy

to

values

of

of

shocks

to

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Perhaps t h e most important parameter f o r the trade-balance/terms-oftrade relation is t h e elasticity of substitution between foreign and domestic
goods.

In t h e benchmark economy, this elasticity i s 1.5; in t h e next two
In t h e large e l a s t i c i t y

experiments we choose larger and smaller values.

experiment (cr=2.5), t h e contemporaneous correlation between net exports and
the terms of t r a d e i s weaker, moving from -0.41 in t h e benchmark case t o
-0.05.

In t h e small e l a s t i c i t y experiment (cr=0.5), the correlation i s more
Evidently the elasticity parameter, cr, has a significant

strongly negative.

influence on this correlation.

In Figure 5,

values of cr between zero and five.
for

small

elasticities

and

positive

we plot

the correlation f o r

We find t h a t the correlation i s negative
for

large

elasticities,

with

the

sign

change occurring a t about cr=2.7.
We get a

more complete picture of

the effect of

the elasticity of

substitution on t r a d e and price dynamics from the cross-correlation

function.

In Figure 6, we report such functions f o r the t r a d e balance and t h e terms of
t r a d e f o r the f i r s t three theoretical economies.
the

three

values

function exhibits a n

of

the

substitution

S-curve.

It

is

We find t h a t f o r each of

elasticity,

clear,

then,

the
that

elasticity does not change this implication of the theory.

function

shifts

to

the

right.

the value of

the

What changing the

as we decrease cr, the

elasticity does is s h i f t the function l e f t and right:
cross-correlation

cross-correlation

Thus,

the

elasticity

of

substitution between foreign and domestic goods a f f e c t s the contemporaneous
correlation between the t r a d e balance and the terms of trade, but not the
asymmetric shape of the cross-correlation function.
This dependence of

the tiining

of

the S-curve

on the

elasticity of

substitution suggests a more subtle interpretation of the data:

t h a t there

is

the

a

relation

correlation

between

function

the

and

timing

the

of

elasticity

the
of

crossing

point

substitution.

of

Studies

crossthat

clevelandfed.org/research/workpaper/index.cfm

estimate t h e elasticity of

substitution between foreign and domestic goods

typically find larger values f o r the United States than f o r Europe and Japan;
see, f o r example, Whalley's (1985, ch. 51 survey of the evidence.

We also

see t h a t t h e cross-correlation function f o r the United States in Figure 1 i s
shifted t o t h e l e f t relative t o those f o r other countries.
work

will

indicate

the

robustness

of

the

relation

Perhaps f u r t h e r

between

these

two

properties.
To this point,

we have considered experiments in which productivity

shocks a r e the only source of
shocks

i s government

fluctuations.

purchases,

which

have

Another potential source of
been

emphasized

contexts by Hodrick (19881, Obstfeld (19891, and Yi (19911.

in

related

In our next

experiment, labeled two shocks, we consider shocks t o both productivity and
government spending.

The parameter values f o r the government

spending

process a r e derived from international data and from Chari, Christiano, and
Kehoe's (19911 estimates f o r the United States.

The mean value of g in each

country i s 2 0 percent of steady-state output, which we have normalized a t
one.

We s e t B = diag(0.95.0.951, so t h a t shocks a r e highly persistent.

innovations a r e assigned standard deviations equal t o 2 percent

of

The
mean

These shocks a r e independent across countries

government spending, o r 0.004.

and of the productivity shocks, a s they tend t o be in international data.
In most respects, the properties of the economy with government shocks
are

similar

to

countercyclical.

those o f

the

benchmark

economy.

Net

exports

remain

The cross-correlation function between net exports and the

terms of trade, pictured in Figure 7, i s f l a t t e r than t h a t with only shocks
t o productivity,

but

has the same general shape.

Introducing shocks t o

government spending, then, does not change these two features of t h e theory.
Thus,

our

theoretical

economy

generates

both

the

countercyclical

movements of net exports and the asymmetrical pattern of cross-correlations

clevelandfed.org/research/workpaper/index.cfm

between net exports and the terms of trade t h a t we see in the data.

With the

benchmark parameter values, however, the dynamics of the theory a r e less
persistent

than

those

in

the

data,

with

the

cross-correlation

function

changing i t s sign one t o two quarters f a s t e r in our theoretical economy than
in the data.

One approach t o this issue is, a s we have seen, t o postulate

smaller values of the elasticity of substitution:

When we lower c from 1.5

t o 0.5 (Figure 6). the point a t which the cross-correlation

function crosses

the axis s h i f t s t o t h e right by one t o two quarters.

Another approach i s t o

consider

examples

additional

dynamic

mechanisms.

Common

range

from

sluggishness in adding new productive capacity (Helkie and Hooper 1988, Junz
and Rhomberg 1973, and Magee 1973 provide typical examples of this story) t o
the fixed costs of changing export quantities of recent work on hysteresis
(Dixit 1989 o r Baldwin and Krugman 1990). We look a t an example of each.
We consider, f i r s t , modifications of the dynamics of capital formation.
Most studies posit either adjustment costs o r multiperiod construction f o r
the technology of capital formation.

Baxter and Crucini (1992) and Mendoza

(19911, f o r example, consider convex costs of

changing t h e capital stock.

Kydland and Prescott (19821, on the other hand, argue f o r "time t o build" and
suggest t h a t a four-quarter construction period (J=4, in the notation of our
theory) is closer t o what we see in the U.S.

economy.

We consider an

intermediate experiment with J=2, labeled time to build in Table 3.
f o r this

experiment,

different

from

modification

the

that

the pattern of

benchmark

economy.

shifts the cross-correlation

cross-correlations
As

we

function

see

in

We find,

is not
Figure

t o the right

much

8,

this

about

one

quarter, bringing the theory closer t o what we see in the data f o r most
countries.
A second modification is a one-period lag in the trading process:

Goods

exported from country 1, say, in period t cannot be used in country 2 until

clevelandfed.org/research/workpaper/index.cfm

period t+l.

We think of t h i s delay as including both time in t r a n s i t and in

clearing customs.
G(alt.blt-l)

and

The Armington aggregators in period t , in t h i s case, a r e
G(alt-l' b I t ),

respectively,

in

the

domestic

and

We label t h i s one-period delivery lag time t o ship.

countries.

This shipping lag introduces a subtle measurement issue:
clear

foreign

what

concept

of

price corresponds

constructing import price indexes.

most

closely t o

One possibility

that

I t i s not
used

in

i s the "delivery" price,

which in our framework would give rise t o a terms of t r a d e in country 1 of
pt

= ~aG~altlblt-l)~ablt-l~~~~G(alt,blt-l)~aalt~.

This relative price corresponds t o t h e value of
customs.

imports once they clear

An alternative i s the "contract" price prevailing at the time the

import goods a r e ordered.

In this c a s e , the equilibrium terms of t r a d e would

be

where

i s the intertemporal marginal r a t e of substitution f o r the domestic composite
good.

We report properties of the l a t t e r definition in Table 3, since this

seems a better approximation of how prices a r e constructed in international
data.
We find t h a t the delivery lag in time t o ship does influence the timing
of the relation between the t r a d e balance and the terms of trade.

We see in

Figure 8 t h a t the cross-correlation function i s shifted t o the right by about
one quarter

relative t o the benchmark economy, again making i t more similar

t o those in the data f o r many countries.

In this sense, both time t o build

and time t o s h i p a r e useful extensions of the benchmark economy.

clevelandfed.org/research/workpaper/index.cfm

V.

Two Extreme Experiments

All of t h e experiments considered in t h e previous section a r e based on
parameter

values

that

we

consider

reasonable.

Here

we

conduct

two

experiments with parameter settings t h a t we regard as unreasonable in order
t o illustrate two central f e a t u r e s of t h e theory.
The f i r s t f e a t u r e i s t h e relation between investment and t r a d e dynamics.
In t h e l a s t section we stressed, as do Brock (19881, Gavin (19901, Matsuyama
(19881,

(19861,

Murphy

and

Sachs

(19811,

the

close

fluctuations in t r a d e and investment in physical capital.
connection, we set t h e capital share parameter

8

connection

between

To emphasize t h i s

equal t o 0.001 in the

experiment labeled no capital, which effectively eliminates capital from t h e
economy.

The behavior of t r a d e and prices changes dramatically.

We find, in

contrast t o t h e benchmark economy, t h a t t h e t r a d e balance i s procyclical and
t h e contemporaneous correlation of
strongly positive.
tent-shaped:

net exports and t h e t e r m s of t r a d e i s

The cross-correlation

There i s no evidence of

economy with capital formation.

function, pictured in Figure 9, i s
t h e S-curve

t h a t appeared in t h e

These differences between t h e economy with

and without capital indicate t h a t capital formation plays a central role in
t h e dynamics of t r a d e and relative prices f o r t h e benchmark economy.
The properties of t h e no capital economy can be understood, f o r t h e most
part,

as

reflections

behavior of trade.

of

consumption

smoothing.

Consider

the

cyclical

We will see in t h e next section t h a t in t h i s economy,

consumption i s less variable than income;

a s a result,

t h e t r a d e balance,

which i s t h e difference between output and consumption at market prices, i s
procyclical.

With respect t o comovements between t r a d e and prices,

dynamic response functions again provide some intuition.

the

A favorable shock

t o domestic productivity leads t o an increase in domestic output, a smaller

clevelandfed.org/research/workpaper/index.cfm

rise

in domestic consumption and,

surplus.

with

these parameter

values,

a trade

With greater output of the domestic good, i t s relative price f a l l s

and t h e terms of t r a d e rises.
correlation

between

the t r a d e

This leads t o a positive contemporaneous
balance

that

decays monotonically

in

both

directions (see Figure 9).
A second f e a t u r e of the theoretical economy i s the dependence of t r a d e
and price dynamics on the type of

shocks hitting the economy.

In the

experiment labeled government shocks, shocks t o government purchases serve as
t h e sole impulse.

With only government shocks we find, again, t h a t the

properties of t h e model a r e much different from our benchmark experiment.
The contemporaneous correlation between net exports and t h e terms of trade,
f o r example, changes from -0.41 in t h e benchmark economy t o 1.00.
most interesting aspect of

these differences concerns t h e cross-correlation

function f o r the t r a d e balance and t h e terms of trade.
spending shocks alone, the cross-correlation
i s tent-shaped:

But the

With government

function, pictured in Figure 9,

I t i s consistently positive, peaks at lag zero, and declines

in both directions.

A s in t h e n o c a p i t a l economy, there i s no sign of a n

S-curve.
Once more we can get some intuition f o r this behavior from t h e dynamic
responses of the economy t o a one-time shock, reported in Figure 10.
striking difference between

government

largely in the response of

investment.

and productivity

shocks

The

shows up

There i s no tendency,

a s with

productivity shocks, f o r a n investment boom t o follow t h e shock; we see, in
fact,

the

between

opposite with
the

economy

these

with

parameter

productivity

values.
and

This sharp

government

difference

spending

shocks

illustrates t h e hazard of predicting comovements between the t e r m s of t r a d e
and t h e t r a d e balance without specifying the shock t h a t gives rise t o these
movements.

Galor and Lin (1991) and Stulz (1988) make similar points in

clevelandfed.org/research/workpaper/index.cfm

different contexts.
This result

i s much different from t h a t

small open-economy

obtained f r o m deterministic

analysis, in which price movements a r e exogenous.

In

prominent papers by Dornbusch (19831, Obstfeld (19821, and Svensson and Razin
(19831, f o r

example,

as

well

as

most

of

the

papers

cited

earlier

in

connection with t r a d e and investment dynamics, t h e source of relative price
movements is not specified.

The relation between t r a d e and relative price

movements, then, i s assumed t o be independent of their source.

This i s

clearly not t h e case in our economy, where price movements resulting from
shocks t o government purchases

a r e associated with much

different t r a d e

responses than those resulting from shocks t o productivity.
In short, the economy generates an S-curve when capital formation is an
important p a r t of t h e propagation mechanism and fluctuations a r e driven by
shocks t o productivity.

Without capital, o r with shocks only t o government

spending, i t does not.

In this sense, both capital formation and t h e source

of price and trade fluctuations a r e critical f a c t o r s in determining the shape
of t h e cross-correlation function f o r net exports and the t e r m s of t r a d e in
our theoretical framework.

VI.

Anomalies
the

cross-

correlation function between t h e t r a d e balance and t h e terms of trade.

Here

We

have

emphasized

the

implications

of

the

theory f o r

w e expand our study t o other properties and point out two discrepancies
between quantitative properties of theory and those of the data.
The f i r s t discrepancy i s evident from Tables 1 and 3:

For our benchmark

parameter values and a wide range of alternatives, the variability of t h e
t e r m s of t r a d e i s significantly smaller in our theoretical economy than i t i s
i n t h e data.

Zimmerman (19911 notes a similar discrepancy in a n analogous

clevelandfed.org/research/workpaper/index.cfm

economy with t h r e e countries of different sizes, as do Stockman and Tesar
(1991) in a n economy with both traded and nontraded goods.

The standard

deviation of t h e terms of t r a d e is 0.48 percent in our benchmark economy (see
Table 3) and 2.92 percent in U.S. data (Table 11, a difference of a f a c t o r of
six.

If we compare t h e theory t o d a t a f o r Japan, t h e difference i s even

larger.

The

difference

is

smaller

if

we

use

a

smaller

elasticity

of

substitution (small e l a s t i c i t y ) o r add shocks t o government purchases (two
shocks), but even in these cases t h e discrepancy between theory and d a t a i s
substantial.

Alternatively, we might argue t h a t the standard deviations of

relative prices in the d a t a a r e overstated.
has constructed improved indexes of U.S.

Alterman

(19911, f o r example,

import and export prices.

Using

these indexes, t h e t e r m s of t r a d e exhibits about 30 percent less variability
than the data used in our Table 1.

We think i t unlikely, however, t h a t

measurement e r r o r i s large enough t o account f o r most of t h e substantial
difference in price variability between theory and data.
A second class of discrepancies concerns t h e magnitude and character of

fluctuations in aggregate quantities:

the standard deviations of consumption

and investment, f o r example, and the correlations of output and consumption
across countries.
parameter

We report these properties in Table 4 f o r all of

settings used

in Table 3.

the

With respect t o the variability of

investment, we found in our earlier study (Backus, Kehoe, and Kydland 1992a)
t h a t when foreign and domestic goods a r e perfect substitutes and goods can be
shipped costlessly between countries, t h e variability of
greater than we see in t h e data.

In U.S. data, reported in t h e f i r s t row of

Table 4, t h e standard deviation of
deviation of output.

investment i s much

investment is 3.15 times the standard

When t h e time t o build parameter J i s one, as i t i s in

the economy of this paper, this ratio is 31.5 (Backus, Kehoe, and Kydland
1992a, Table 5).

We approximate this economy in the experiment labeled

clevelandfed.org/research/workpaper/index.cfm

perfect

substitutes, where

standard deviation of
t h e benchmark

we

s e t cr=100 and w =w
1 2'

investment, relative t o t h a t of

economy,

however,

In t h i s case,

the

output, i s 30.3.

In

investment i s much

standard deviation, relative t o output, i s 3.48.

less variable:

Apparently,

The

t h e concavity

of technology implied by imperfect substitutability, even f o r values of cr a s
large a s 2.5 (our l a r g e e l a s t i c i t y experiment), i s sufficient t o bring t h e
theory close t o the data in this respect.

For this reason, we do not view

investment variability a s an anomaly of the theory.

A more robust discrepancy i s what we termed, in our earlier paper, t h e
consumption/output

anomaly:

In the data, the correlation of

consumption

across countries is generally smaller than t h a t of output; in our theoretical
economies,

we see the reverse.

In d a t a f o r the United

S t a t e s and

an

aggregate8of European countries, f o r example, the consumption correlation i s
0.46, the output correlation 0.70;
perfect

substitutes

economy,

see the data row of Table 4.

these

correlations

are

0.67

In our

and

-0.58,

respectively, s o there is clearly a large difference between theory and data.
With

imperfect

benchmark

substitutability

experiment,

for

between

example),

foreign
the

and

domestic

consumption

goods

correlation

(the
(0.77)

remains substantially larger than the output correlation (0.021, although the
difference between them is smaller.

Complementarity between foreign and

domestic goods reduces this discrepancy even more (see the small e l a s t i c i t y
experiment, in which cr i s reduced t o 0.5 from 1.5 in t h e benchmark case), but
does not eliminate it.
regard

using

nontraded

Stockman and Tesar (1991) do somewhat better in t h i s
goods

and t a s t e

shocks,, but

they

understate

the

correlation across countries of consumption of traded goods alone.
In short, work t o date has documented two robust discrepancies between
properties of the d a t a and those of this class of theoretical economies.
f i r s t concerns relative price variability:

The

The terms of t r a d e appears much

clevelandfed.org/research/workpaper/index.cfm

more variable in t h e d a t a than in the theoretical economies.

The second

concerns international comovements:

In t h e theory, we generally find that

the

countries

correlation

consumption;
opinion,

of

output

across

is

in the d a t a we see the reverse.

are

two

of

the

central

issues

in

stronger

than

that

These anomalies,
international

of

in our

business

cycle

research and stand as clear challenges t o future work in this area.
The question in t h e present context is how these anomalous features
a f f e c t our assessment of the dynamics of the t r a d e balance and the terms of
trade.

This i s probably impossible t o answer without knowing how those

anomalies a r e resolved.

Nevertheless,

we suspect t h a t t h e countercyclical

movements in t r a d e and the S-shaped cross-correlation function f o r t r a d e and
relative

prices

primarily

may

be robust

properties

on t h e persistence of

of

productivity

the theory,

since they

rely

shocks and the dynamics of

capital formation, features t h a t apply t o a much broader class of economies
than ours.

Thus, we suspect that this account of the S-curve may survive the

changes t h a t are called f o r by anomalies in other dimensions of the model's
properties.

VII.

Concluding Remarks
This

study

adds

to

a

growing

literature

in

which

international time series d a t a a r e compared t o those of
equilibrium models.

properties

of

dynamic general

Prominent examples include Baxter and Crucini (19921,

Cardia (19911, Mendoza (19911, and Stockman and Tesar (1991); Backus, Kehoe,
and Kydland (1992b) provide a more complete list.
wide range of issues.

These studies look at a

The f i r s t three papers, f o r example, examine the

correlation between saving and investment rates within countries.

Stockman

and Tesar (1991) study, among other things, the correlations of output and
consumption across countries.

W,e add t o this list a consideration of the

clevelandfed.org/research/workpaper/index.cfm

short-run dynamics of t r a d e and relative prices.
theory mimics the cross-correlation

We find t h a t while the

function f o r t h e t r a d e balance and the

terms of trade, in two other respects the theory d i f f e r s sharply from the
data.

Future work should tell us how these discrepancies between theory and

d a t a a r e resolved and how f u r t h e r developments bear on the dynamics of t r a d e
and relative prices.

clevelandfed.org/research/workpaper/index.cfm

REFERENCES
William Alterman,
in P. Hooper
Transactions:
University of

"Price trends in U.S. trade:
New data, new insights,"
and J.D. Richardson, eds., International Economic
I s s u e s in Measurement and Empirical Research, Chicago:
Chicago Press, 1991.

Paul Armington, "A theory of demand f o r products distinguished by place of
production," I M F Staff Papers, 27 (19691, 488-526.
Jacques Artus, "The 1967 devaluation of the pound sterling," I M F Staff
Papers, 22 (19751, 595-640.
David Backus, Patrick Kehoe, and Finn Kydland, "International real business
cycles," J o u r n a l of Political Economy, 101 (August 1992a1, 745-775.
David Backus, Patrick Kehoe, and Finn Kydland, "International business
cycles: theory and evidence," unpublished manuscript, August 1992b.
Richard Baldwin and Paul Krugman, "Persistent t r a d e effects of large
exchange r a t e shocks," Quarterly Journal of Economics, 104 (November
1990). 635-654.
Marianne Baxter and Mario Crucini, "Explaining saving/investment
correlations, " American Economic ~ e v i e w ,forthcoming 1992.
Keith Blackburn and Morten Ravn, "Contemporary macroeconomic fluctuations:
An international perspective," unpublished manuscript, January 1991.
Philip Brock, "Investment, the current account, and the relative price of
non-traded goods in a small open economy," J o u r n a l of International
Economics, 24 (19881, 235-253.
Emanuela Cardia, "The dynamics of a small open economy in response t o
monetary, fiscal, and productivity shocks," J o u r n a l of Monetary
Economics, 28 (December 19911, 411-434.

V.V. Chari, Lawrence Christiano, and Patrick Kehoe, "Optimal fiscal policy
in a business cycle model," unpublished manuscript, Federal Reserve Bank
of Minneapolis, September 1991.
Jean-Pierre Danthine and John Donaldson, "Methodological and empirical issues
in real business cycle theory," unpublished manuscript, 1991.
Alan Deardorff and Robert Stern, Computational Analysis of Global Trading
Arrangements, Ann Arbor: University of Michigan Press, 1990.
Avinash Dixit, "Entry and exit decisions under fluctuating exchange rates,"
Journal of Political Economy, 98 (June 19891, 620-638.
Rudiger Dornbusch, "Real interest rates, home goods, and optimal external
borrowing," Journal of Political Economy, 91 (February 19831, 141-153.
Oded Galor and Shoukand Lin, "Terms of trade, interest rates, and current
account dynamics, " unpublished manuscript, Brown University, January
1991.

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Michael Gavin, "Structural adjustment t o a terms of t r a d e disturbance: The
real exchange r a t e , stock prices, and t h e current account," J o u r n a l of
Internationa l Economics, 28 (May 19901, 217-243.
John Hassler, P e t t e r Lundvik, Torsten Persson, and Paul Soderlind, "The
Swedish business cycle: Stylized f a c t s over 130 years," unpublished
manuscript, Stockholm, 1992.
William Helkie and Peter Hooper, "An empirical analysis of t h e external
deficit, 1980-86," in R. Bryant, G. Holtham, and P. Hooper, eds.,
External Deficits and the Dollar: The Pit and the Pendulum, Washington:
Brookings Institution, 1988.
Robert Hodrick, "U.S. international capital flows:
Perspectives from
rational maximizing models," Carnegie-Rochester Conference S e r i e s on
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Helen Junz and Rudolf Rhomberg, "Price competitiveness in export trade among
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Finn Kydland and Edward Prescott, "Time t o build and aggregate fluctuations,"
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Brookings P a p e r s on Economic Activity, 1: 1973, 303-323.
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The Harberger-Laursen-Metzler effect," Journal of Political Economy, 91
(February 19831, 97-125.
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APPENDIX
Data Sources a n d Definitions
The d a t a used in Table 1 and Figures 1 and 2 were taken from the
Organization foy ~ c o n o m i c Cooperation and Development's Quarterly National
Accounts.

These a r e reported quarterly in a publication of the same name;

our numbers come from a machine-readable d a t a base supported by the Board of
Governors of t h e Federal Reserve System.

real output:
output in base-year
on t h e country;
net exports in current prices:

The variables of interest a r e

prices, either GNP o r GDP, depending

exports minus imports in current prices;

terms of trade:
ratio of the implicit price deflator f o r imports t o
the implicit price deflator f o r exports, with deflators computed a s
r a t i o s of current-price imports and exports t o base-year-price
imports and exports.

The sample periods noted in Table 1 a r e the complete samples from the January
1991 version

of

the

data b a s e .

We

seasonally

Australia, Austria, and Finland using the X-11 method.

adjusted

the

data

for

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Table 1
Properties of Net Exports, Real Output, and the Terms of Trade
in 11 OECD Countries
Std. Deviation
(percent)

Autocorrelation

Correlation

Country
-

-

Australia
Austria
Canada
Finland
France
Germany
Italy
Japan
Switzerland

U.K.
U.S.
Median
Definition of Variables:
nx = the ratio of net exports to output
y =the logarithm of real output
p = the logarithm of the ratio of the import deflator to the export deflator
NOTES: Data are quarterly, from the Organization for Economic Cooperation and Development's Quarterly NationalAccounts. Numbers in
parentheses are Newey-West standard errors. All statistics refer to Hodrick-Prescottfiltered variables. Sample periods are Australia,
1960:IQ-1990:IQ; Austria, 1964:IG1990:IQ; Canada, 1955:IQ-1990:IQ; Finland, 1975:IQ-1990:IQ;
France, 1970:lQ-1990:IQ; Germany,
1968:lQ-1990:IQ; Italy, 1970:ICT1990:IQ; Japan. 1955:llQ-1990:IQ; Switzerland, 1970:ICT1990:IQ; United Kingdom, 1955:lQ-1990:IQ; and
United States. 1950:IQ-1990:llQ.
SOURCE: Authors' calculations.

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Table 2
Benchmark Parameter Values

Preferences

P

Technology

8 = .36, 6 = .025,J = 1,

= .99, p = .34, y = -1.0

a = ll(l+p) = 1.5, import share = -15

Forcing processes
A =

[I:

var

=

6:

g, = 0.

SOURCE: Authors' calculations.

var

.906 .088
= I.088 . g o d
E; =

.00852*, corr(e:,e$) = 258

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Table 3
Properties of Net Exports, Real Output,
and the Terms of Trade in Theoretical Economies
-

Std. Deviation
(percent)
Economy
Benchmark

m

Y

-

-

Autocorrelation

P

m

Y

Correlation

P

(my)

(%P)

-.41
.49
(.08) (.14)

(Y,P)

-30 1.38
-48
(.02) (.18) (.06)

.61
.63
-83
(.07) (.lo) (.05)

-.64

Large Elasticity

.33 1.41
.35
(.03) (. 18) (-05)

.63
.64
.88
(.07) (.18) (-03)

-.57 -.05
.43
(.08) (.09) (.14)

Small Elasticity

.37 1.33
.76
(.03) (.18) (.07)

.61
.63
.77
(.07) (.lo) (.05)

-.66 -.80
.51
(.07) (.09) (. 16)

Two Shocks

.33 1.33
.57
(.03) (.IS) (.07)

.62 .65
.78
(.08) (.08) (-06)

-.57 -.05
.39
(.15) (.17) (.17)

Time to Build

.28 1.34
.51
(.02) (.17) (.06)

.60 .63
.52
(.17) (.lo) (.16)

-.61
-.40
.50
(.07) (.08) (.12)

Time to Ship

.24 1.35
-48
(.02) (. 18) (.05)

.65 .66
.66
(.07) (.08) (.09)

-.56 -.51
.61
(.08) (.09) (.11)

No Capital

.18 1.14 1.29
(.Ol) (.15) (.09)

.71
.61
(.06) (. 11)

Government
Shocks

.16
.17 -30
(.03) (.02) (.05)

.67 .67
.67
( 1 1 (.08) (.ll)

Perfect
Substitutes

16.90 2.22
(1.14) (.29)'

---

-.lo
(. 18)

.76
(.05)

-64
(.07)

---

(.07)

.66
(.06)

.99
.68
(.OO) (.06)

-.55
1.00 -35
(.13)
(.13) (.OO)
.10

(.w)

---

---

NOTES: Statistics are based on Hodtick-Prescott filtered data. Entries are averages over 20 simulations of 100 quarters each; numbers in
parentheses are standard deviations. Parameters are as in Table 2, except for large elasticity, o = 2.5; small elasticity, o = 0.5; two shocks,
2
mean of g = diag (0.2,0.2), B = diag (0.95,0.95), and Vg = diag (0.004 ,0.004~);government shocks, as in two shocks plus z, = 1, all t; time
to build, J = 2; no capital. 0 = 0.001; time to ship, one-period shipping lag, as described in the text; and perfect substitutes, 0 = 100, and import share = 0.5.
SOURCE: Authors' calculations.

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Table 4
Business Cycle Properties of Theoretical Economies
Ratio of Std. Dev. to
mat of Output
Economy

c

x

Data

.49

Correlation
(c,Y>

(x,Y)

3.15

.76

.90

.70

.46

.31
(-06)

30.32
(1.07)

.75
(.12)

.01
(.05)

-.58
(. 15)

.67
(. 17)

Two Shocks

.62
(.09)

4.29
(.59)

.78
(.ll)

.89
(.04)

.00
03)

.83

Time to Build

.49
(.08)

3.35
(-30)

.88
(.06)

.93
(-02)

.04
(. 18)

-77
(. 10)

.72
(. 11)

-

.42

.79

Perfect Substitutes

@I,Y~) ( ~ 1 ~ ~ 2 )

Benchmark

Large Elasticity

Small Elasticity

Time to Ship

No Capital

Government Shocks

.93

3.66

-.95

-.95

Definition of Variables:

c = the logarithm of real consumption
x = the logarithm of real fixed investment
y = the logarithm of real output
Subscripts 1 and 2 refer to the domestic and foreign countries, respectively.

NOTES: Parameter values are described in Tables 2 and 3. The data row is taken from Backus, Kehoe, and Kydland (1992a, Table 5);
entries refer to the United States, except for the correlations between foreign and domestic output and consumption, which refer to the
United States and Europe. As in Table 3, numbers in parentheses are standard deviations of the relevant statistic over 20 simulations of 100
periods each.
SOURCE: Authors' calculations.

33

,

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Figure 1
Correlation of p

t

and n x
t+k

Australia

Austria

Japan

0.75

0.00
--25
-.50
--7s

-.25
-.75

.

.

.

.

-

.

-

-

-

-

-

.

.

-

Switzerland

Finland

0.75

United Kingdom
0.25
0.00

- -2s
-.50
-.75

-7

-3

I

5

-25

-.so

- .75

-7

-3

-7

-3

1

United States

Fmnce

! !$[

-.50
- .75

1

Germanu

SOURCE: Authors' calculations.

5

5

.

.

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Figure 4
120

Dynamic Responses to Domestic Productivity Shock

,

i

.
\

.OUTPUT
..

**.

-.*

*

-- - - -.- -

------ -- - -------

-------____
-----------------P

R

D SHOCK
~ ~

O

-------------------

0-

TERMS OF TRADE

/

..
.

1.00

t

0.80-

INVESTMENT

'b,

t
t

'.

0.60 -

z

P

%

...
..'.

Oa40-

CONSUMPTION

-

a

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

*=-.__

0.20 -

-

G

----------__-______
-----------

.
0

2

0
1

!
2

/
3

:
4

,

5

,
6

,

,
7

,
8

,

9

,
10

,
11

,

,
12

,
13

QUARTERS

SOURCE: Authors' calculations.

,
14

,

,

15

16

,

,
17

,
18

,,
19

,
20

,
21

,
22 23

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Figure 10
Dynamic Responses to Domestic Government Shock

0.90

I

0.75 0.60 -

GOVERNMENT SPENDING

0.45 -

S
P
a

Os300.15 -

5

-- -- --OUTPUT
--

-- -- -- -- -- -- __

0.00

4

0

-- -

- - - ----TERMS OF TRADE

-0.15-

-- -- -- __

----

.

0

3

1

0

2

1

3

4

i

~

5

6

1

7

,

8

t

9

t

10

1

~

11 12 13

0.00
-0.05 -

C
C C
C
C

CONSUMPTION

0

1

2

3

4

5

C

4 -

6

7

8

9

10

11 12

--

t

15

t

16

8

17

t

18

19

4--

13

14

~

20

~

21

t

22 23

_ -- -- _--- --

----

C

QUARTERS
SOURCE: Authors' calculations.

~

14

15

16

17

18

19

---

20 21 22 23

8

r

~

t