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working paper
department
of
economics
COMPARATIVE ADVANTAGE AND THE
CROSS-SECTION OF BUSINESS CYCLES
Aart Kraay
Jaunie Ventura
98-09
June, 1998
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
WORKING PAPER
DEPARTMENT
OF ECONOMICS
COMPARATIVE ADVANTAGE AND THE
CROSS-SECTION OF BUSINESS CYCLES
Aart Kraay
Jaume Ventura
98-09
June, 1998
MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASS. 02142
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SEP
1 6 1998
LIBRARIES
Comparative Advantage
and the
Cross-section of Business Cycles
Aart Kraay
Jaume Ventura
The World Bank
M.I.T.
May, 1998
Business cycles are both less volatile and more synchronized with the
in rich countries than in poor ones. In this paper, we develop two
alternative but non-competing explanations for these facts. Both explanations
proceed from the observation that the law of comparative advantage causes rich and
poor countries to specialize in the production of different commodities. In particular,
rich countries specialize in "high-tech" products produced by skilled workers while
poor countries specialize in "low-tech" products produced by unskilled workers.
Cross-country differences in business cycles then arise as a result of asymmetries
among the industries in which different countries specialize. We focus on two such
asymmetries. The first we label the "competition bias" hypothesis, and is based on
Abstract
:
world cycle
in production costs are more prevalent in hightech industries, sheltering producers from foreign competition and therefore making
the idea that cross-country differences
them
The second asymmetry we
based on the idea that production costs in
might be more sensitive to the shocks that drive business cycles.
large suppliers
in
the markets for their products.
label the "cyclical bias" hypothesis,
low-tech industries
and
is
Comments are welcome at akraay@worldbank.org (Kraay) andjaume@mit.edu (Ventura). The views
expressed here are the authors' and do not necessarily reflect those of The World Bank.
Business cycles are different
Figure
1
,
we have
and poor
in rich
as the
Volatility
fluctuations in per capita
ones.
In
GDP growth against
sample of countries. We refer to this
plotted the standard deviation of per capita
the log-level of per capita income for a large
relationship
countries. In the top panel of
Graph and note
that
it
is
income growth are smaller
the bottom panel of Figure
1
we have
,
downward-sloping, meaning that
countries than
in rich
poor
in
plotted the correlation of per capita
income growth rates with world average per capita income growth (excluding the
country
in
countries.
question) against the log-level of per capita income for the
We
refer to this relationship
is
self-explanatory,
shows
in rich
in
Both explanations
countries than
in
poor ones. Table
that these facts are quite robust.
causes
rely
on the notion
that
it
is
per capita income growth are more
1
,
which
1
Here we develop two alternative but non-competing explanations
facts.
set of
as the Comovement Graph and note
upward-sloping, meaning that fluctuations
synchronized with the world cycle
same
that the law of comparative
these
for
advantage
rich countries to specialize in "high-tech" industries that require sophisticated
technologies operated by skilled workers, while poor countries specialize
in
"low-tech"
industries that require traditional technologies operated by unskilled workers. This
pattern of specialization
opens up the
possibility that cross-country differences in
business cycles are due to asymmetries between high-tech and low-tech industries.
For instance, assume that production
foreign
shocks and less sensitive
immediately that production
in
to
in
high-tech industries
domestic shocks than
in
is
more
low-tech ones.
high-tech industries, and therefore
would be more synchronized with the world cycle than
in
sensitive to
in rich
it
is
reasonable to expect that foreign shocks are less
domestic shocks. As a
countries,
1
result,
would also be less
Acemoglu and
reference to the
Zilibotti
production
volatile
in
than
volatile
many
other
than
in rich
low-tech ones.
(1997) also present the Volatility graph.
graph.
Comovement
countries,
high-tech industries, and therefore
in
follows
low-tech ones. Moreover, to
the extent that foreign shocks are an average of the domestic shocks of
countries,
It
We are unaware of any previous
One
explanation of
idea that producers
in
in
low-tech industries.
why
industries react differently to
asymmetry among
refer to this
industries as the
"competition bias" hypothesis. This bias would occur, for instance,
production costs
among
more prevalent
firms are
differences
in
These cost
and make them
large
international markets.
in
how
This competition bias has implications for
and foreign shocks. Consider the
unit costs in
in
if
high-tech industries.
in
differences shelter technological leaders from their competitors
suppliers
based on the
is
more market power than producers
high-tech industries enjoy
We
shocks
all
effects of
industries react to domestic
a favourable domestic shock that reduces
industries. Since producers in high-tech industries are large suppliers
international markets, increases
in their
production lower prices, moderating the
effects of the shock. Since producers in low-tech industries are small suppliers in
world markets, increases
in their
production have
the extent that the competition bias
is
important,
little
To
or no effect on their prices.
one would therefore expect
that
high-tech industries are less sensitive to domestic shocks than low-tech industries.
Consider next the effects of a foreign shock that raises production and income
abroad and, as a
result,
increases
tech industries are large suppliers
into
a large
and
prices. Since
shift in their industry
producers
in
demand
in
in all industries.
international markets, this
demand which
in
world
demand
is
low-tech industries are small suppliers
met by increases
that the competition bias is important,
industries are
more
in
in
production
international
demand as most of
production abroad.
one would therefore expect
To
high-
translated
is
in
in
the
the extent
that high-tech
sensitive to foreign shocks than low-tech industries.
Another explanation
the idea that unit costs
business cycles than
in
in
for
would occur
if
why
industries react differently to
the latter might be
the former.
the "cyclical bias" hypothesis.
this bias
shock
leads to large increases
markets, this shock has a negligible effect on their industry
increase
Since producers
If
We
more
sensitive to the
refer to this
shocks
is
based on
shocks that drive
asymmetry among
industries as
business cycles are driven by productivity shocks,
industry productivity
is
more
volatile in
low-tech industries.
If
business cycles are driven by monetary shocks,
advance constraints are more prevalent
this bias
cash-in-
if
for firms in low-tech industries.
This cyclical bias also has implications for
and foreign shocks. Almost by assumption, the
domestic shocks reduce
might arise
how
industries react to domestic
cyclical bias implies that favourable
more than
unit costs in low-tech industries
high-tech
in
industries, leading to larger increases in production in the former than in the latter.
This
is
how
the cyclical bias explains
why
high-tech industries are less sensitive to
domestic shocks than low-tech industries. Less obviously, the
more
implies that high-tech industries are
industries.
To see
this,
sensitive to foreign
cyclical bias also
shocks than low-tech
consider the effects of a favourable shock that raises
The
production and income abroad.
cyclical bias implies that
worldwide production of
low-tech products increases relative to that of high-tech products, raising the relative
price of high-tech products.
constitutes a favourable
one
From the perspective
shock
for low-tech producers.
for
As a
domestic economy,
of the
this
producers of high-tech products and an adverse
result, high-tech industries
are
more
sensitive to
foreign shocks than low-tech industries.
To analyze these
issues
we
construct a stylized world equilibrium model of the
cross-section of business cycles. Inspired by the work of Davis (1995),
world
in
which differences
in
both factor
industry technologies a la Ricardo
endowments a
combine
to
la
economy
determine a country's comparative
to both the sort of productivity fluctuations that
emphasized by Kydland and Prescott (1982), and also
real effects since firms
and
find conditions
cyclical
biases can be used to explain the evidence
enough
that
we
to
face cash-in-advance constraints.
cross-section of business cycles
obtain closed-form solutions for
also find that our results hold even
in
we
all
We subject this
have been
monetary shocks
that
have
We then characterize the
under which the competition and
in
Figure
1.
The model
is
simple
the expressions of interest.
We
the presence of trade frictions, modelled here
as "iceberg" transport costs, provided that these
the pattern of trade. Also,
consider a
Heckscher-Ohlin and
advantage and, therefore, the patterns of specialization and trade.
world
we
frictions
are not so large as to alter
find that reductions in transport costs (globalization?)
magnify cross-country differences
in
business cycles.
hypotheses under consideration have
of the
terms of trade.
In principle,
between the two hypotheses.
Finally,
we show that the two
different implications for the cyclical properties
these properties can be used to distinguish
In practice,
however, a
first
look at the data yields
conflicting evidence.
The research presented here
economy
real
is
related to the large literature
on open-
business cycle models, surveyed by Backus, Kehoe and Kydland
(1995) and Baxter (1995), that explores
how
productivity
shocks are transmitted
across countries. Our work also relates to recent work by Obstfeld and Rogoff
(1
995,
1998) and Corsetti and Pesenti (1998) that analyzes the international transmission of
monetary shocks.
We differ from these
emphasizing the aspects
focus on those aspects
in
in
lines of
research
in
two ways. Instead of
which business cycles are similar across countries,
which they are
different. Instead of
focusing primarily on
the implications of international lending, risk-sharing and factor
transmission of business cycles,
The paper
is
we emphasize
the role of
organized as follows. Section
1
we
movements for the
commodity
trade.
2
develops the basic model.
Section 2 explores the properties of a cross-section of business cycles
in
the basic
model. Section 3 extends the model by introducing money. Section 4 further extends
the model by introducing transport costs. Section 5 examines
the
model
for cyclical properties of the
some
implications of
terms of trade. Section 6 concludes.
Previous literature on business cycles in open economies typically assumes that either (a) there is a
so that there is no commodity trade whatsoever, or (b) that countries are completely
specialized in the production of differentiated products. Whether such models provide a good
description of observed trade patterns has not been a major concern for this literature. In contrast, the
model presented here is empirically consistent with the main features of observed trade patterns: (a) a
large volume of trade among rich countries in products with similar factor intensity (intraindustry trade);
(b) substantial trade among rich and poor countries in products with different factor intensities
(interindustry trade); and (c) little trade among poor countries.
single commodity,
1.
A Simple Model
of Trade
and Business Cycles
We consider a world with a continuum
which
industries,
skilled
and
country
is
refer to
unskilled workers
defined by a
an index
of productivity.
country differences
in
and
is,
one; two
8
is
in their
technologies, their
of production,
endowments
their level of productivity. In particular,
triplet (n,8,7i),
technology of the country
mass
as the a- and p-industries; and two factors
unskilled workers. Countries differ
and
of skilled
we
of countries with
where
jj.
is
a measure
of
each
how advanced
the fraction of the population that
is skilled,
the
and n
is
We assume that workers cannot migrate and that cross-
technology are stable, so that
)i
and 8 are constant.
We
generate business cycles by allowing the productivity index n to fluctuate randomly.
The
a-
and
p-industries
each contain a continuum
measure one which can be traded
of differentiated products of
at zero cost. Firms in the a-industry
sophisticated technologies that require skilled labour, while firms
traditional
in
use
the p-industry use
technologies that can be operated by both skilled and unskilled workers.
we
Not surprisingly,
shall find that rich countries that
have better technologies and a
high proportion of skilled workers export mainly cc-products, while poor countries that
have worse technologies and a high proportion
products.
To emphasize
instruments.
To
the role of
simplify the
commodity
problem
further,
of unskilled
trade,
we
we
workers export mainly p-
rule out trade in financial
also rule out investment. Jointly,
these assumptions imply that countries do not save. 3
Preferences
Each country
level of skills
3
and
populated by a continuum of consumers
js
who
differ in their
personal opportunity cost of work, or reservation wage.
their
The model presented here
is
related to Kraay
and Ventura
(1
997).
We
index consumers by
this
ie [1/y, 00 )
Pareto distribution:
P(i)
and assume
= 1 - (y
maximizes the following expected
c a (z,i)
E|U
•
\)~
X
with ?t>0, y>0.
,
is
distributed according to
A consumer with
index
i
utility:
\
1-v
nV
that this index
cp(i)
e -P-t.dt
K|)
1-v
(1)
i
/
where
if
the
U(.) is
any well-behaved
of a-
is
an indicator function
that takes value
e
e
e-i
1
= Jc a (z,i)
1
and p-products:
_
c«(i)
l(i)
otherwise; and ca (i) and c p (i) are the following
consumer works and
consumption indices
function;
e
e-1
e-i
"•I
dz
cp(i)
=
Jcp(z,i)
e
e-1
-dz
(2)
_o
where ca (z,i) and c p (z,i) are consumer
industries, respectively.
The
i's
consumption of variety z
elasticity of substitution
of the a-
between industries
one, while
is
the elasticity of substitution between any two varieties within an industry
and p-
is 9,
with
e>i.
The
spend a
solution to the
fraction
Moreover, the
v of
their
ratio of
consumer's problem
is
quite straightforward.
income on a-products and a
fraction 1-v
spending on any two a-products z and
z' is
Consumers
on p-products.
given by
1-e
1-e
Pp(z)
Pa(z)
;
and the
ratio of
spending on any two p-products z and
z' is
Pa(z')
Pp(z')
where p a (z) and p p (z) denote the
respectively. Finally,
unskilled)
price of variety z of the a-
consumers work
if
exceeds a reservation wage
and only
1
of
i"
.
if
and p-products,
the applicable
wage
(skilled or
We
express
prices
all
terms of the ideal consumer price index,
in
1-v
V
"1
Jp a
1
(z)
"1
Te
-e
-dz
J
to
P p(z)
1
1-e
-
and
of skilled
assumption that the
1
Let
.
r(p.,8,7i)
and
w(|j.,8,7t)
be the wages
j
unskilled workers
be the measure
=
d2
.0
.0
of skilled
i.e.
in
and
a
(p.,8,7i)-country. Also,
define
s(u.,8,7t)
unskilled workers that are employed.
distribution of skills
and
u(u.,8,rc)
Under the
and reservation wages are independent, we
have that
i
s
=
r
\
8-
(3)
(
i
u
= (1-6)
w\
x
\
(4)
1
Equations
(3)-(4)
f
'
r
show
\^ x
employed are
y,
that type of
enough so
'
and
w
unskilled workers that are
wage
any type
worker
respectively.
If
the
the entire labour force of that type
is
employed and the labour supply
v
reaches
and
that the fraction of skilled
l
,
workers becomes
"k,
is
the
vertical.
happens.
that this never
labour supplies,
of
of
y)
J
same
Throughout,
Finally,
we
we
shall
assume
that y
is
for
large
note that the wage-elasticity of the
for both types of
workers since
it
only depends on the
dispersion of reservation wages.
Firms and Technology
The
to
all
oc-industry
uses sophisticated production processes that are not available
and
e~ ta
countries
that require skilled workers. Let
practice" unit labour requirements to
produce one
'
products of measure dz. Let
(1
+ Ti)e _£flc
n
unit of
'
n
dz (ea>0) be the "best-
a given small set of a-
dz (rpO) be the "second-best"
technology available
measure
dz. Let
owns
country
in
produce one
be the measure
unit of
a given small set of a-products of
of a-products in
the best-practice technology.
how advanced
products
\i
to
the technology of a country
which a firm located
We can
interpret
Assume
is.
in
a
(|a,8,7i)-
a natural indicator of
u.
further that the set of a-
which two or more firms share best-practice technology has measure
1
zero. Jointly, these assumptions imply that
1
=
1
Ju. dF(|j.,8)
•
J
where
,
F(u.,8) is
the
oo
time-invariant joint distribution function of
ti is
large
enough so
facto'
monopolists
policy
is
to set
in
that the firms that
a markup over
£«
We shall
their unit cost.
Symmetry ensures
same
price,
skilled
and
same
4
all
wages are
firms
Symmetry ensures
that
high
all
in all
unskilled workers. In particular,
have access
competitive and prices are equal to costs.
that in equilibrium skilled
all
firms
in
(5)
p-products of measure dz. Since
P-products.
that that
p-industry uses traditional technologies that are available
is
that
p a (p.,8,7i):
workers of any kind are required to produce one
p-industry
assume throughout
n
and can be operated by both
the
8.
the market for their products. Therefore, their optimal pricing
Pa=^r.e-
(e p >0)
and
have the best-practice technology are 'de
the a-industry of a (ji,5,7i)-country set the
The
p.
enough
unit of
to the
countries
e~
p
n
-dz
a given "small" set
same
of
technologies, the
We shall assume throughout
that only unskilled workers
firms in the p-industry of
a
produce
(^,8,7i)-country set
price, p p (n,8,7t):
Pp=w-e"
Epn
Two features
(6)
of this representation of
throughout the paper.
First,
technology play an important role
the elasticity of substitution
8
among
varieties 6 regulates
the extent to which the competition bias
is
important.
is
If
perceived as different (similar) by consumers and, as a
face
weak
6->°°, the
low (high), a-products are
result, firms in
the a-industry
(strong) competition from producers of other varieties of a-products.
degree
As
and the competition bias
of competition in the a-industry increases
disappears. Second, the parameters e„ and ep regulate the importance of the
cyclical bias.
If
e a <£p (£a>£p), unit costs in the (3-industry (a-industry) are
sensitive to fluctuations
As
in productivity.
more
£a->£p, the cyclical bias disappears.
Productivity Fluctuations
We
generate business cycles by assuming that the productivity index
fluctuates randomly. In particular,
we assume
that
component, n, and a country-specific component,
% consists
of the
components are independent across
specific
components
n n
interval
2'2
respectively,
,
with zero
where n
is
a
that the productivity index
drift
variance reflected on the interval
and 0<a<1
.
These assumptions imply
n-*,n +
*
2
2
This interval
time as the global component of productivity changes. Finally,
and country-specific components
on the
interval
4
5
n n
5
.
of productivity, G(IT)
We assume that the
initial
itself
it
is
and
unit
fluctuates over
a well-known
and
G(7t-n), are uniform
cross-sectional distribution of
is the case if the share of spending on a-products not too small,
See, for instance, Harrison (1990), Chapter 5.
This
drift
Brownian motion that the invariant distributions of the
global
2'2
and country-
Brownian motions on the
follows a Brownian motion with zero
result of the theory of reflected
global
and instantaneous variances odt and (1-o)dt
positive constant
it
a global
that the country-
countries. Both the global
of productivity are reflected
of
We assume that the
n-Yl.
and country-specific components are independent, and moreover
specific
sum
i.e.
v»0.
the country-specific
component
of productivity
and hence does not change over
From the perspective
of
time.
a
instantaneous correlation between these shocks
regulates the extent to which the variation
whether
i.e.
shows possible sample paths
n under three
panel,
first
we assume
country-specific.
all
in
the variation
%
is
so that
is
in
n
is
global,
The
i.e.
changes
third
in
straightforward to
Vo7
is
it
6
.
That
n
comes from dn
different
is
n are
in
in
show
that the
the parameter
is,
is
due
n
n and
a
to the global
or d(7t-n). Figure 2
assumptions regarding
constant and
The second panel shows the case
global productivity, n.
variation in
that o=0,
It
changes
refer to
domestic productivity
in
or country-specific components,
the
we can
(u.,8,7t)-country,
as as domestic and foreign productivity shocks.
of
equal to the invariant distribution
is
the variation
all
a. In
in
%
is
which c=1 Then, djr=dn and
.
perfectly correlated with
panel shows the case
in
changes
which 0<o<1 Then, the
.
has both country-specific and global components.
Equilibrium Prices and Trade Flows
Let p be the average price of an oc-product (or the ideal price index of the
industry) relative to the
of the p-industry).
average price of a p-product product
Then, our normalization
1
-e
1
"1
1-e
= p1
-dz
(or the ideal price index
rule implies that
1
"1
(z)
Jp a
cc-
"v
and
.0
Jp p
(z)
1
-e
1-e
-dz
=p
v
.
Using
this notation, the
.0
equilibrium prices of
any a-product and p-product produced
1
Pa=X"P
1-v
V-
in
a
(jj.,5,7t)-country are:
1+A.
0+ *.
e
e+x.
e a (7t-n)
(7)
This will be true except when either n or n are reflected at their respective boundaries. These are rare
events since the dates at which they occur constitute a set of measure zero in the time line.
10
Pp = P
where %
is
_V
(8)
7
a positive constant. Since each country
varieties of a-products, the price of these varieties
many
quantity produced. Countries with
productivity (high 71-n) producing
quantities of
prices disappears
in their
must command the same
not be produced
p = vK-e
is
\\f
of varieties (low
in
equilibrium. Finally,
(e 0" £a)
'
and p a—>p
we
its
own
5) with relatively high
1 "
result,
v
.
In
p.)
produce large
face low prices. As 8->oo,
the p-industry
all
products
price. Otherwise, low-price varieties of (3-products
find that the equilibrium
would
value for p
is:
n
(9)
another positive constant.
(£a>£p)» high productivity is
8
the presence of a cyclical bias,
In
e^ep
associated with high (low) relative prices for a-products as
the world supply of p-products
the cyclical bias disappears
by the
workers (high
a small number
of
depends negatively on the
each variety of the a-products and as a
the dispersion
where
skilled
a "large" producer
is
is
high (low) relative to that of a-products.
and the
As
£a-»£p,
relative prices of both industries are unaffected
level of productivity.
fi_i
7
In particular,
=
x
Tn^l e+x
-
11
J
JJji-
-~ o o
^S
(uT (1+x e a
)'
—
-e
(7l_n)
dF(y,8)dG(jt- n) which
,
constant given that the distributions F and
G
are time-invariant.
To
derive Equation
on the (sum of all) a-products of a (u,5,7i)-country and a
productions. Second, use Equations (3)-(6) to find that:
of world expenditure
of the value of
P«' = Pre
•
•
e e+ ^
is
j
a
.
Finally, substitute this
(7),
equate the
(u',8',7t')-country to
expression
in
ratio
the ratio
the ideal price index of
U-5'J
the cc-industry and solve tor p„. Equation (8) is simply a consequence of our normalization rule and the
observation that all p-products command the same price in equilibrium.
R+i
1+1
8
In particular,
\v
v
=
v
(
e
\
x
°°
J
1-v V.O-V
(1+A.)-e
11
J
J(1
-
5)
e
R
p
-(7i-n)
dF(u, 8) dG(n - n)
^00
derive Equation (8), we equate the ratio of spending in both industries to the ratio of worldwide
production of both industries and then use Equations (3)-(7) to solve for p.
To
11
Let
industry,
y(|a,5,7i;)
i.e.
and
y=rs+wu and
technologies (high
u.)
values for both y and
countries. Since
be the income and the share
x(|i,8,7t)
x=
r
•
s
Not surprisingly, countries with good
.
and a high proportion
We therefore
x.
of skilled
consumes
of a-products
and import almost
all
of them,
all
all
number
infinitesimal
countries export almost
of their
consumption
income, these exports and imports are x and
5)
have high
To balance
it
as
of varieties of
all
rich
cc-
of their production
of a-products.
v, respectively.
usually referred to as intraindustry trade, since
with similar factor intensities.
workers (high
refer to countries with high values of x
each country produces an
products and
production of the a-
in
As a share
This kind of trade
involves two-way trade
their trade, countries with
in
of
is
products
x<v export p-
products and countries with x>v import them. As a share of income, these exports
and imports are v-x and
x-v, respectively.
This kind of trade
interindustry trade or factor-proportions trade.
stylized
manner
a large volume
industry trade
As a
is
result, the
usually referred to as
model captures
in
a
three broad empirical regularities regarding the patterns of trade: (a)
of intraindustry trade
between
rich
and poor
among
rich countries, (b) substantial inter-
countries,
countries.
12
and
(c)
little
trade
among poor
2.
The Cross-section
In
to
the world
two kinds
supplies.
On
of Business Cycles
economy described
of shocks.
On
the
in
the previous section, countries are subject
one hand, domestic
productivity
shocks
the other hand, foreign productivity shocks shift industry
shift industry
demands.
In
the presence of the competition bias or the cyclical bias, these shocks have different
effects in high-tech
similar
shocks
and low-tech
differs
industries.
As a
result,
the aggregate response to
across economies with different industrial structures.
In
other
words, the properties of the business cycles that countries experience depend on the
determinants of their industrial structure, that
is,
on
their factor
endowments and
technology.
Domestic and Foreign Shocks as a Source of Business Cycles
The (demeaned) growth
rate of
income
in
a
(n.,8,7i)-country
a linear combination of domestic and foreign shocks:
dlny-E[dlny] = ^ E dn + ^n
The
functions ^(\i,8,n) and
l,
can be written as
9
dn
(10)
n (\i.,b,n)
measure the
sensitivity of
a country's
growth rate to domestic and foreign shocks, and are given by:
$K=<1 + *.)-
xe
Q
x e
'
To see
prices
this,
apply
and supplies
Ito's
in
9-1
f
+X
+ (1-x)-e p
+
«"rr^
W+A
lemma
(
x " v)(e «
to the definition of
Equations
(11)
_e P
)
income and use the expressions
(3)-(9).
13
(12)
for equilibrium factor
Equations (10)-(12) provide a complete characterization of the business cycles
experienced by a
(ji,8,7t)-country.
how business
Moreover, they show
cycles differ
across countries, since the sensitivity of growth rates to domestic and foreign shocks
depends on the share
in
production of high-tech products,
detrended growth rate of world average income, Y,
dlnY-E[dlnY] =
where the
co
sensitivity of the
is
Finally,
x.
we
note the the
given by
n dn
(13)
world growth rate to innovations
in
component
the global
of productivity is given by:
©n=(1 + A.)-(v-e a +(1-v):e p
Let
country,
denote the standard deviation of the growth rate of a
V(u:,8,jt)
and
let C(|i,8,7i)
denote the correlation of
income growth. These are the
graphs
we
in
Figure
(i)lf
w
(ii) If
(iii) If
10
1
:
Q
+X
e
+X
en > e„
a
P
eR
w
statistics:
is
V=
then
,
- o)
—=—=
then
—— <
and
-— >
Z,
we have
n +a
(t,
x.
Moreover:
all x;
—— >
for
all x;
and
dx
and
—
-
<
for
all x.
dx
3x
A.
•
for
on
at most,
dx
dx
simple, since
y(l
and Comovement
10
dx
< e„
The proof
then
,
+
growth rate with world average
theoretical analogs to the Volatility
The functions C and V depend,
=£«•-—-,
£3
H
its
closed-form solutions for both the
K + £n
)
and
C=
volatility
and comovement
.
,
V(i-o)-§! +«•(£* +Sn)
does not depend on
x,
(^1,8,71)-
Using the Equations (10)-(14) and the properties of the shocks,
1.
derive the following result:
PROPOSITION
(14)
)
V
(C)
will
be downward (upward) sloping
proposition describes the sign of
for different
if
and only
parameter values.
9x
14
if
^
is
Since
^+£n
2
decreasing
in x.
The
This
is
the
as measured by
of
first
x, to
theoretical Volatility
a series of results that relate a country's
the properties of
its
business cycles. Proposition
if
show
same parameter
that this
implies that rich countries are less sensitive to domestic shocks
remainder of
Why Are
sensitive to foreign shocks
this section
their
the competition bias (low 8) and/or the cyclical bias (ep>£a)
are strong enough. Equations (11)-(12)
more
says that the
1
and Comovement graphs have the same slopes as
empirical counterparts
with x), but
industrial structure,
we
(i.e.
E,
n
is
(i.e.
£, n
increasing with
restriction
is
decreasing
x). In
the
provide intuition for this result.
Rich Countries Less Sensitive To Domestic Shocks?
Domestic shocks
shift industry supplies.
When
these shocks are positive,
they raise production,
wages and employment
they lower production,
wages and employment. However,
in
both industries.
When
negative,
to the extent that the
competition bias and the cyclical bias are important, these effects are larger
in
the p-
industry than the a-industry.
It
useful to start with a
is
benchmark case
in
which 6->«> and Ea=Ep=£, so that
neither the competition bias nor the cyclical bias are present.
productivity
industries,
shock
results in
and has two
an increase
in
productivity of
familiar effects. Holding constant
productivity directly raises production
by
productivity also raises the
wages
employment, output and income
to the
growth rate of income
elasticity of the labour
shares
their
is
sum
and
rise further.
in all
is
nothing but the
i.e. e-drc.
Increased factor
a
result,
This contribution of employment growth
wages,
countries by the
15
both
employment, increased
unskilled workers and, as
measured by Xedm, and
in
e-drc in
of the growth rates of productivity
production,
in
of skilled
supply to changes
therefore raise growth rates
magnitude
and hence income. This
celebrated Solow residual and consists of the
of both sectors, weighted
A favourable
X.
its
strength
depends on the
Favourable domestic shocks
same
magnitude,
i.e.
(1+X)edn.
To see how
shocks,
assume
the competition bias determines
that G
is finite
and ea=e p =e. As
domestic shocks raise productivity equally
employment and
output. This
since the country
is
large
is
in
a-products are met with reductions
in
the a- and p-industries, raising wages,
its
a-products, increases
^—
•
demand faced by each
share of the a-industry (the larger
prices. Since rich countries
effects
on
their
have larger
growth rates,
i.e.
(1
+
more important
the
cc-industries,
X)
1
shocks,
assume
a-industry by
residual
Ea-dic,
and
in
and
and the employment
on
converse
their
will
growth rates,
be
To sum
Now
larger
is this stabilizing
is
the
role of
•
how a
country responds to domestic
domestic shocks raise productivity
As a
be smaller
effect will
and the
is 0)
e drc
•
the p-industry by fy-dn.
industry. Since rich countries
effects
£c<ep.
The more
9 + KJ
the cyclical bias determines
that 0-»°<>
.
domestic shocks have smaller
-x
V,
To see how
•
+ A.
cc-product (the lower
is x),
e drc
•
the supply of
in
and income. This
prices that lower production
9
inelastic is the
as before. However,
(1+A.)-£-djt
measured by the term -x
stabilizing effect of prices is
country reacts to domestic
benchmark case, favourable
the
captured by the term
the markets for
in
in
how a
in
result,
in
the
both the Solow
the a-industry than
in
the p-
have larger a-industries, domestic shocks have smaller
i.e. (1
+ a)
•
[x e a
+ (1 - x) epl dn
•
-
.
Clearly,
if
£a>£P the
,
true.
up,
in all
countries domestic productivity shocks shift outwards the
supplies of a- and p-products. Since rich countries produce mainly high-tech
products, they face inelastic industry
experience relatively small
effects of
virtue of
demands
(i.e.
the competition bias) and
shifts in supplies (i.e. the cyclical bias).
domestic shocks on income are small
in rich
countries.
As a
domestic shocks are large
in
in
supplies. This
poor countries.
16
is
why the
the
Poor countries, by
producing primarily low-tech products, face elastic industry
experience relatively large shifts
result,
effects
demands and
on income
of
Why Are
Rich Countries More Sensitive to Foreign Shocks?
Foreign shocks
shift industry
production and income
Whether this leads
on the extent
abroad.
To
to
to
in
demands. For instance,
demand
the rest of the world, increasing
an increase
in
which the increase
the
in
demand
demand
for the
positive
for
all
products.
domestic industry depends
met by an increase
is
shocks raise
in
production
the extent that the competition bias and the cyclical bias are important,
the increase
in
demand
the
always larger than that
for the a-industry is
of the
(3-
industry.
It
is
benchmark case
useful to start again with the
competition bias nor the cyclical bias are present,
foreign shock consists of an increase
edn
the domestic economy.
First,
it
and
9->«>
Ea=ep=e.
average productivity abroad
in
both industries and therefore raises worldwide
in
both a- and p-products. However,
in
i.e.
which neither the
in
demand and
of
A favourable
magnitude
production of
follows from Equation (12) that this has no effect
The reason
is
simple and follows from three assumptions.
the assumption of homothetic preferences ensures that, at given prices, the
demands
relative
for both types of products are unaltered
as income grows. Second,
the assumption that £a=£p ensures that, at given prices, the relative supplies of both
industries are unaltered as productivity grows. Third, our assumption that 0->°°
ensures that consumers are very
willing to switch their
over different varieties of products. The
increases
demands
third
in
first
two assumptions
for both industries. This is
varieties of cc-products, there are
To see how
assume
why p does
in
that 9
is finite
demands
since the increase
no changes
not
in
in
and
ea=ep=e.
It
that the
in relative
(recall
how a
is still
Equation
in
(9)).
The
supplies of different
prices.
country reacts to foreign
true that after a favourable
the foreign supplies of both industries match exactly
at the industry level.
demand
change
in their relative
the competition bias affects
foreign shock the increases
the increase
mean
the foreign supplies of both industries match exactly the increase
assumption means that despite the change
shocks,
consumption expenditures
for
As a
result
domestic cc-products
17
is
p
is
not
not affected. However,
matched by increased
production abroad, the price of these varieties increases. This stimulates wages,
employment and production
x
—
•
•
e drc
and
,
in
the a-industry. This effect
more
larger the
is
inelastic
the
is
is
measured by
demand faced by each
a-
+ A,
product (the lower
Since
their
is 6)
rich countries
larger
the share of the a-industry (the larger
is
have larger a-industries, foreign shocks have larger
is x).
on
effects
growth rates.
To see how
assume
shocks,
foreign
its
and the
that 0->c»
and
e a <s p
.
At given prices,
shock raises the world supply of oc-products
demand. As a
there
result,
is
an excess demand
supply of p-products that leads to an increase
point of view of the country, this
industry
and a decrease
shifts raise
the (3-industry.
(1
+ A.)
-
(x
v) fep
•
- e a ) and
effects
To sum
Since
the
Since
on
its
their
whose
effects of foreign
foreign
whose
((3-products)
(recall
domestic
in
sign
and an excess
Equation
demand
(9)).
for the
(5-industry.
From the
domestic
the a-industry, while lowering
is
shocks
shift
the
(i.e.
measured by
is
a net exporter
shocks
larger a-industries, foreign
demands
of both industries at
face
with the world cycle
stiff
home.
little
the competition bias) and specialize
shocks are positive and
price
them
growth rates.
move
result,
cc-
These demand
depends on whether the country
have
favourable
by less (more) than
for a-products
the
in
we have now that a
have a larger share of high-tech products, they have
prices
products and, as a
p
country reacts to foreign
effect in both industries
competition from foreign suppliers
products
for the
rich countries
up, foreign
rich countries
industries
an increase
demand
The combined
of a- or p-products.
have larger
in
is
in
wages, employment and production
in
•
how a
the cyclical bias determines
large.
(i.e.
the cyclical bias).
As a
shocks are less positive than
in rich
cycle.
countries,
negative.
18
result,
Poor countries produce low-tech
competition form abroad and specialize
moves against the world
in
As a
result,
in
the effects of
and they might even be
The Role
of
In this
Commodity Trade
model, the properties of business cycles
because countries have
many
different industrial structures,
differ
as measured by
determinants of the industrial structure of a country.
the most important of such determinants, that
we deny this
ability to
is,
%^ =
(1
+ X)
perhaps
ability to trade. In fact,
In
a world of autarky, x=v
In
in
if
every country and
such a world the
growth rates to domestic and foreign shocks would be the
v ea +
•
Comovement graphs would be
C^Vc
We focus here on
a country's
commodity prices are determined by domestic conditions.
countries,
There are
x.
the countries that populate our theoretical world, their business
cycles would have identical properties.
sensitivities of
across countries
(1
- v) eg
flat,
and
•
V
^=
=(1 + X)-
;
and the
same
Volatility
V£ a +(1-V)£p
in all
and
and
7
.
Moving from a world
of autarky to
a world of free trade affects the
industrial
structure of countries since in free trade the relative prices of those products
a country has comparative advantage are higher than
higher industry shares, even
if
in
in
autarky. Higher prices imply
production remains constant. But one would also
expect higher prices to stimulate employment and production. These increases
employment could come from unemployment, as
here.
case
Or they could come from employment
if
we changed
which
in
is
the case
in
in
the model presented
other industries, as
it
would be the
our assumptions and allowed both industries to use both types of
workers.
11
This result depends on the assumption that the elasticity of substitution between a-products and pproducts is one. Otherwise, industrial structures would also be different in autarky and the cross-section
of business cycles would exhibit some variation.
19
3.
Monetary Policy
In this
we
section
extend the model by introducing monetary shocks as an
additional source of business cycles fluctuations.
money and business
simplification is
cycles,
adequate
if
we assume
shocks
shocks
one takes the view
to the marginal
money
to the rate of
is
customary
monetary policy
that
other than stabilizing the cycle. For instance,
public good,
As
if
that
We
advance
the inflation tax
used
is
their
a country
if
money by assuming
In particular,
firms
is
committed to
is
in
the country are
monetary authorities use
have
to
that firms face
use cash
in
a cash-in-
order to pay a fraction of
before production starts. Firms borrow cash from the
government and repay the cash plus
output
a
the exchange rate.
12
wage payments
to finance
value of this public good are translated into
growth. Alternatively,
motivate the use of
constraint.
This
monetary policy has objectives
translated into shocks to the nominal interest rate, as the
manage
the literature on
is erratic.
maintaining a fixed parity, shocks to foreign investors' confidence
the latter to
in
interest after production
is
completed and
sold to consumers. Monetary policy consists of setting the interest rate on
cash, and then distributing the proceeds or losses
consumers. Increases
in
in
a lump-sum fashion among
the interest rate raise the financing costs of firms, reducing
wages, employment and output.
formally equivalent to supply
In this
model, interest-rate shocks are therefore
shocks such as changes
in
production or payroll taxes.
The Model with Money
Let
countries,
i
be the
interest rate
each country
is
now
on cash. Since monetary
defined by a quadruplet
process for interest-rate shocks following the
12
See
Christiano,
Eichenbaum and Evans (1997)
for
same
20
(n,8,7t,i).
steps
a discussion
policy varies across
We construct the
we used
of related
to construct the
models.
process
for productivity
shocks
in
Section
independent pieces: a global component,
1
The
.
I,
interest rate
consists of two
i
and a country-specific component,
i-I.
Moreover, the country-specific components are independent across countries. Both
component and the
the global
Brownian motions on the
reflecting
instantaneous variances
and
0<())<1.
with zero
country-specific
and
<|>-dt
i
interval
and
unit
of interest rates are
i
,
2'2
with zero
respectively,
(1 -<J))dt
These assumptions imply
drift
components
where i
that the interest rate
i is
is
a positive constant
a Brownian motion
l
t
variance reflected on the interval
and
drift
l
T
2
The
cross-sectional distribution of the country-specific components, H(i-I),
i
i
and hence does not change over
2'2
country,
we
is^.
that their correlation coefficient
shocks are assumed
The
is
Equations
to
is
uniform on
of
a
and note
foreign interest-rate shocks
Finally, productivity
shocks and
(u.,8,7i,i)-
interest-rate
be independent.
introduction of
of the model.
problem
and
define di and dl as domestic
From the perspective
time.
initial
2
monetary policy leads
to
minor changes
in
the equilibrium
Since cash-in-advance constraints only affect firms, the consumer's
not altered
(3)-(4)
payments k„ and
and both the spending
remain
valid.
Kp in the a-
Regarding
and
and the labour supplies
in
we assume that a fraction
of
rules
firms,
have
p-industries
to
be made
in
wage
cash before
production starts. Consequently, the costs of producing a small set of products of
measure dz include not only the
e~
z
V'
n
-dz, but also the financing costs, e
Equations
(5)-(6)
p a=
13
unit labour requirements,
have
JL.
r
to
'
l
dz and e
'
K
Kpl
-dz.
dz and
13
As a
result,
be replaced by:
.e—
We are using the following
Ka
e~ Za
l
(15)
approximations here: Ka-i^lnO+Ka-i) and Kpi=ln(1+KP
21
i).
^
pl
pp
=w-e
An
interesting novelty of the
source
potential
industries,
i.e.
(16)
for the cyclical bias.
£a=ep unit costs could
,
in-advance constraint
Even
still
more binding
is
extension of the arguments
valid,
model with money
in
Section
if
productivity
be more
1
-V
{ep
p=
-e
« )n
¥ .e
-^
is
there, Kp>K„. Finally,
1
it
indicates another
equally volatile
can be used
this
As
the cash-
that Equation (8)
is still
14
(17)
Kp " KjI
'
(
(18)
Equations (15)-(18) are natural generalizations of Equations
(9).
if
both
a straightforward
show
to
in
«*
-e~
{fj
that
volatile in the p-industry
while Equations (7) and (9) must be replaced by:
Pa=x-P
is
the cash-in-advance constraints
model converges
to the
become
less important,
model without money presented
i.e.
(5), (6), (7)
k^->0 and Kp-»0,
Section
in
and
1
Properties of Business Cycles
With the addition of interest-rate shocks, income growth
country
14
"1
15
given by this generalization of Equation (10):
The constants % and
X
¥
is
=
J
o+i
+x
e
i+i
+x
i
x
\\t
are
HH^
J
=
v
1-v
(
r
now given
G
-
e
b
^
\?-V
co
;
j
(|i,8,7i,i)-
15
'«*
[(i+X)E -(7t-n)-x-K
11
JJ(1
_ 6) e V
.
R
P
V
.dF(^8).dG(K-n).dH(v-I)
-(i-i)J
B
P
>*.dF0i.8).dG(7t-n).dH(i-i)
^o-^rjO
To compute income, remember that
but a transfer from firms to
the
by:
e8+X
co
in
consumers
financing costs are not really a cost for the
via the government.
22
economy as a whole
dlny-E[dlny] =
where
and
^(h,8,tc,i)
£,(11,8,71,1) ,
^
d7c
dn-^ di-^
+ §n
and £ n (|-i,S,7t,i) are
which measure the
dl
defined by Equations
still
sensitivity of
(19)
(1
income growth
1)-(12)
to
and
^(|j.,8,7t,i)
domestic and
foreign interest-rate shocks, are given by:
5i
= \-
Si
=
1-
X-K„
a
Equations
(1
+ (1-X)Kp
Q
+X
1
+1
(20)
(21)
Q+X
1)-(12)
business cycles of a
£i->0
e-1
XK„a
and
(19)-(21) provide a complete characterization of the
(u.,8,7t,i)-country.
As
k^O and Kp->0, we have that £,->0 and
and business cycles are driven only by
we have
shocks.
that
In
Z, K
-^>0
and
i;
n ->0
productivity shocks.
As e„->0 and
and business cycles are driven only by
Ep->0,
interest-rate
the general case, however business cycles result from the interaction of
both type of shocks.
A comparison
and
foreign
mentioned
of (20)-(21
)
with
monetary shocks are very
earlier,
differences
in
(1
1)-(12) reveals that the effects of
similar to those of productivity shocks.
(21)
as e„ and ep do
in (1 1)
monetary shocks only have
and
with
is
smaller,
i.e.
i.e.
Ka and Kp play the
(12). In contrast to productivity
indirect effects
wages and labour supplies. Therefore,
shocks
As
the prevalence of cash-in-advance constraints
provide an alternative source of cyclical bias,
and
domestic
on production through
same
role in (20)
shocks, however,
their effects
on
the sensitivity of income growth to monetary
the term (1+X) which premultiplies (11) and (12)
is
replaced
A,.
Since
we now have two sources
of
business cycles, world average growth
given by:
23
is
dlnY-E[dlnY] =
where
con is
a> I
If
still
k rp = k„
a
Q
+X
w
Kn > k„
a
p
Q
+X
Q
+X
If
functions
then
,
is
given by:
(23)
,
then
C and V
-— = —— =
dx
—
—
,
Proposition 2
then
for
<
and
—
—
x.
16
Moreover:
all x;
>
for
all x;
and
dx
>
and
<
for
all x.
dx
dx
is
depend, at most, on
result:
dx
dx
kr < k„
p
co,
shocks are negligible ea=ep=0, we have the following
productivity
w
(n)
(22)
+(1-v).Kp]
=A.-[v-K
:
(ii) If
n dn-(0[ dl
defined by Equation (14) while
PROPOSITION 2 The
(i) If
co
the natural analog to Proposition
1
in
a world
in
which
business cycles are driven only by interest-rate shocks. The competition and cyclical
biases cause cross-country differences
in
business cycles, regardless of whether the
cycles are driven by productivity shocks or interest-rate shocks.
the competition bias
of
16
and the
cyclical bias
generate these patterns
business cycles has been discussed at length
i!
Note that
The
proof
is
in this
case
analogous
v-j[i-.).{?,..( t ,.{,)
to that of Proposition
The
1
24
in
in
intuition of
why
a cross-section
Section 2 and need not be
M dc..
kMM
r
we
repeated here. Instead,
productivity
shocks and
PROPOSITION 3 The
:
generalize Propositions
interest rate
functions
and 2
1
to the
case where both
shocks drive business cycles, as
C and V depend,
at most,
on
x.
follows:
Moreover,
if
17
av
—
<
3x
(
—
>0), then
— >0 (—
3x
3x
<0). Define:
3x
0-1
(
?
?
"\
A = (1-a)-0+*r-|e o -Q^-epJ-ep+(1-*)-*
(
-I
6-1
-^-^-K p ^
Ka
Kp
;
J-
B=
(1-c).(1 + X)
2
{e„.^I-e p )
.£!-«,
+ (l-«.»? .(«.
J
Then,
A>0,
(i) If
—
>
for
all x;
3x
(iij if
-B<A<0,
— <0 (— >0)
—
3x
(iii) if
if
x<--
<
A<-B, then
for
(x>--);and
B
dx
B
all x.
3x
and
Proposition 3 provides a set of necessary
functions
V and C
to exhibit the
be the highest value
for x in
same
slopes than their empirical counterparts. Let x*
a cross-section of countries. Then, a necessary and
sufficient condition for
business cycles to be less
the world cycle
countries
in rich
sufficient conditions for the
is
that
volatile
A+Bx*<0. This
and more synchronized with
condition
is
always
both types of shocks generate industry responses with the right biases,
17
C
Note that
V = ^(1-c)-^ + a-£ n + Sn)
+(1-4>K?
2
+4>-(Si +Sl)
^,,+^n
+**»?)-((1-oK|
nor %,+tn depend on
decreasing (increasing)
x,
V
in x.
(C)
The
is
+o(U +S n
2
)
and
Since neither
+(1-4>K
downward (upward)
sloping
2
if
2
+<MSi +^i)
and only
proposition describes the sign of
—
3x
different
parameter values.
25
if
i.e.
a-«>n"ten + Sn> + *- m i-($i-HJi)
=
y(o-o>ft
is
2
satisfied
1(1
v
if
(1
- o)
•
)
- o)
Z,
-i,
n +
2
n +
(1
-
(1
<|>)
•
-
£,
•
<t>)
x
I
'
2
%x
for
and Kn > k„
£r > En
instance,
it
.
But
might be that the cc-industry
(interest-rate)
this is not
is
shocks and less sensitive
more
less volatile
6+
A,
P
>K a
-), yet
6+
be less sensitive
shocks and more sensitive
6-1
-—
,
(e
p
>e a
—
6-1
-
still
business cycles are
A.
and more synchronized with the world cycle
(productivity)
shocks
6—1
(k r < K a
naturally requires that the cc-industry
K
sensitive to domestic productivity
to foreign productivity (interest-rate)
6—1
than the (3-industry, £r < e a
a necessary condition. For
to
in rich
countries. This
domestic interest-rate
to foreign interest-rate (productivity) shocks,
,
).
26
4.
Trade Integration
The postwar
barriers to
period has seen large reductions
commodity
instead explore
how
trade.
Here we do not attempt
parametric reductions
of business cycles. Throughout,
in
we assume
in
both physical and policy
to explain
these changes but
transport costs affect the cross-section
that transport costs are small
relative to cross-country differences in factor
endowments
that
all
enough
countries are either
net importers or net exporters of the p-product, for any value of their domestic
productivity
assume
and
and
interest rates,
for
that transport costs are small
technology
in
possible equilibrium prices. Moreover,
all
enough
relative to cross-country differences in
the a-industry that every a-product continues to be produced
one country. These assumptions ensure
that the pattern of trade
introduction of transport costs, although the
we
volume
of trade
is
is
in
only
unchanged by the
negatively related to
the size of transport costs.
Remember that the main theme
of this
cycles a country experiences depends on
decline, the prices of products
increase and, as a
result, the
natural conclusion of this
in
its
paper
is
that the nature of business
industrial structure.
As
which a country has comparative advantage
share
argument
in
is
production of these industries increases.
that
one should expect
We confirm
A
that reductions in
transport costs (globalization?) increase the cross-country variation
of business cycles.
transport costs
in
the properties
this intuition here.
The Model with Transport Costs
We
generalize the model with
costs of the "iceberg" variety,
i.e.
if
money by assuming
that trade incurs transport
t>1 units of output are shipped across borders,
only one unit arrives at the destination while x-1 units "melt"
Pp(z)
now denote
in transit.
Let p«(z) and
the f.o.b. or international price of variety z of the a-products and of
27
the p-products, respectively.
of these international prices,
relative to p-products.
We
use the same normalization
and define p as as the average
The presence
as before
In
each country, the
imports and import-competing products are higher than the
f.o.b.
c.i.f.
measure
u.
P-products
do not produce, the
of domestically-produced a-products
is
xpp(z)
if
the country
is
c.i.f.
is x-
a net importer
price of
all
terms
or
prices of
c.i.f.
prices while the
prices of exports are equal to the f.o.b. prices. Since countries import
varieties of a-products they
in
a-products
f.o.b. price of
of transport costs implies that the
domestic product prices vary across countries.
c.i.f.
rule
all
the
but the infinitesimal
p a (z). Similarly, the
of p-products,
c.i.f.
price of
and p p (z)
otherwise.
Note that the consumer continues
(evaluated at
prices) over
c.i.f.
labour supply decision
is
in
terms of a
reservation wage. However, since
c.i.f.
consumption expenditures
commodities exactly as before. The consumer's
also unchanged:
applicable wage, expressed
different
to allocate
prices, the price of
a
consumers work
unit of
in different
is
given by x
Therefore,
we need
(
s
=
the country
if
to replace
countries face
in
a
(u.,8,7r,i)-country.
This
Equations
(3)-(4)
by the following generalizations:
^
r
r
(
their
a net importer of the p-product, and x otherwise. 18
5-
= (1-8)-
the
v
is
(24)
YPc
u
if
consumption now varies across countries.
Let p c (n,8,rc,i) denote the ideal price index of consumption
index
and only
consumption, exceeds
consumers located
unit of
if
w >
-?-
X
(25)
U-Pcy
18
To see this, use the normalization rule and recall that all countries import all but the infinitesmal
number of a-products produced domestically, and so incurr the transport cost on (almost) their entire
consumption of a-products, which constitute a fraction v of total expenditure. In addition, consumers in
countries that are net importers of p-products face a c.i.f. price of xp for their remaining expenditure on
p
P-products.
28
Since a-products are exported
and
is
f.o.b. prices
only valid
and, as a
countries, producers face identical
in all
Equation (15)
result,
countries that export p-products.
in
the producer price of these products
is
T-p p and,
,
However, Equation (16)
is still valid.
In
c.i.f.
countries that import p-products,
as a
result,
Equation (16) has to be
replaced by:
T-p
=w-e"
p
E
P-
7C+K
replace 8 and
1
-8 with 8
and with 5-t
products,
l
(26)
somewhat tedious algebra
Straightforward but
for equilibrium prices in
P
Equations
•
x~
4v
x
(8),
and x
•
(1
(17)
and
- 8)
and (1-8)-t~*"
still
hold, provided that
the country
if
v
(18)
reveals that the expressions
otherwise.
is
we
a net importer of p-
19
While trade patterns are unchanged, the world economy with transport costs
exhibits less cross-country variation in industrial structures than the world
with free trade.
industries in
The higher
the transport costs are, the lower
is
the price of those
which the country has comparative advantage. That
price of a-products (P-products)
before, this leads to
(poor) countries.
in rich
an reduction
in
economy
is,
the lower
(poor) countries. For the reasons
is
the
mentioned
the share of the cc-industry (P-industry)
in rich
20
19
To derive the analog to Equation (17), we can equate the ratio of world expenditure on the (sum of
a-products in any two countries to the ratio of the value of productions as before. Using the new
expressions for wages in the expressions for factor supplies results in
all)
1
(..,<!
u'-6
Pa' = Pa
-A.
pC
1+x
x
Wi
„M
Q+X
^•
a-(*- )-77r K
K
A
e H+
/-
..
e
n,
H-6p c
of our
.
Inserting this in the ideal price index
,
for the a-industry yields the appropriate modification of
consequence
a-(i-i')
1
•
unchanged normalization
rule.
To
Equation (17). Equation (8)
is
simply a
obtain the analog to Equation (18), note
first
that
the presence of transport costs implies that the market -clearing conditions in the a- and p-lndustries
can now be expressed as equating the value of world production at producer prices to the value of world
consumption
at
consumer
new expressions
prices for
for factor prices,
all
a-
and the
and p-products. Then, using the analog to Equation (17), the
factor supplies we can equate the ratio of expenditure in both
industries to the ratio of productions at producer prices to obtain the appropriate modification of (18).
It is straightforward to verify this by substituting the expressions for equilibrium wages and
20
employment
into the definition of
x and differentiating with respect to
29
x.
Business Cycles and Transport Costs
The (demeaned) growth
and
to
rate of
income
(19)-(21). Consequently, Proposition
a country's
volume
industrial structure
of trade and,
as a
result,
still
3
is still
given by Equations
relating the properties of
A
in
the cross-sectional dispersion
process of parametric reductions
are important,
we know
that the Volatility
and upward sloping with
volatility of
volatility in
costs
in
in x.
This implies that
the model with transport
in
transport costs has opposite effects on
x,
If
the competition and cyclical biases
and Comovement graphs are downward
respectively. Therefore, reductions
business cycles
in rich
in
transport costs
countries (as their x increases)
poor countries (as their x decreases). Similarly, reductions
make business
(as their x increases)
their
business cycles
the free-trade model.
the business cycles of rich and poor countries.
lower the
1)-(12)
holds. However, transport costs reduce the
the cross-section of business cycles exhibits less variation
costs than
(1
cycles
and
more synchronized
with the world cycle
less synchronized with the world cycle
x decreases).
30
in
in
and
raise
transport
in rich
countries
poor countries (as
5.
Terms
of Trade Shocks
In this section,
we develop
implications of the theory for the cross-section of
changes
the (growth of the) terms of trade. Often,
to
be exogenous
to the
in
model, as part of the description of the "shocks" to the
system. The advantage of a world equilibrium model
freedom by determining the behavior
of the
We exploit this feature
cyclical bias hypothesis
have
structure of a country. Although
empirically distinguish
somewhat
here to
different implications for
of the (growth rate of the)
in
that
is
terms of trade
sources of fluctuations.
comovement
assumed
the terms of trade are
in
show
how
it
removes
that the competition
the
volatility
principle these implications could
first
of
terms of more primitive
terms of trade vary with the
between our two hypotheses, a
degree
this
and
and
industrial
be used
to
look at the data yields
inconclusive results.
Properties of the
Terms
of Trade
Let T(ji,8,n,i) denote the terms of trade of a (u.,8,7i,i)-country, defined as the
ideal price index of production relative to the ideal price index of
refer to the (detrended) growth rate in the
trade shock.
21
Using the expressions
consumption.
terms of trade of a country as
for prices in
Equations
(8)
and
its
We
terms of
(19)-(20), this
is
given by:
dlnT-E[dlnT] = 5l
21
-dJt
+ sS -dn-£ T -di-Sj"
-dl
that the growth rate of T in (27) is equivalent to the growth rate in the
weighted by the share of exports in income, less the growth rate of the
ideal price index for imports weighted by the share of imports in income. We use this alternative
It
is
straightforward to
show
ideal price index for exports,
formulation
when we
turn to the data.
31
(27)
where
^/(|a.,8,7i,i)
of trade to
and £ n
T
measure the
(|i,5,7t,i)
sensitivity of the
domestic and foreign productivity shocks, while
measure the
growth
T
^, (^,5,7c,i)
the terms
in
and
T
^, (^,5,7i,i)
domestic and foreign monetary shocks, and are given by
sensitivity to
^=-x-e«~
^ =x
'
£a
'iTX
$7=-X-K a
+(x " v)
'
" ea)
(£p
(29)
—^-
e7=xk„
The
(28)
(30)
i-(x-v)(k r -K„)
intuitions for
(31)
these expressions should be
familiar.
Increases
in
domestic
productivity (decreases in domestic interest rates) raise the supply of domestically-
produced varieties
decline
price
in their
constituting
of the a-products.
If
the competition bias
as countries are "large" suppliers
an adverse terms
of trade
shock
for the
present, this leads to a
is
in their
export markets,
domestic economy. This
is
captured by Equations (28) and (30), which vanish as 0->«> and the competition
effect disappears. Increases in foreign productivity
rates) raise the
demand
raise their price
as well (See Equation
trade shock for
all
for
a-products
countries,
share of a-products
in
and
is
in all
(17)).
(decreases
in
countries and provided that 6
is finite,
This constitutes a favourable terms of
larger the richer
is
a country
(the larger
is its
production). In addition, provided that ea<£p (Ka<Kp), foreign
shocks create an excess demand
for
all
an increase
all
a-products (See Equation
in
foreign interest
the relative price of
a-products relative to (3-products, leading to
constitutes a positive (negative) terms of trade
a-products with x>v (x<v).
32
shock
(18)).
This
for net exporters (importers) of
Empirical Implications
Let
VT (fi,8,7t,i)
terms of trade of a
denote the standard deviation of the (detrended) growth of the
(u.,5,7t,i)-country,
world average output growth.
Comovement and
We
let
C T (u.,6,7t,i)
We
:
[(1-o)-e a +(1-(t»)-K a
E = a-(e p -e a
)
+<t>-(icp
correlation with
its
as the Terms of Trade
have the following
PROPOSITION 4 The functions CT and VT depend,
D=
denote
refer to these statistics
graphs.
Volatility
and
result:
at most,
on
22
x.
Define:
].^;
-K a )
;
M = a-(1 + ?,)-[v-e a +(1-v)-ep]-(£p-e a
)
+ (j)-X-[v-K a +(1-v)Kp]-(Kp-K a )
Then,
T
(i)
T
E
8V
3V
—
x<v—
(^>0)if
(x>v—E— );and
^-<0
D+E
D+E
3x
3x
(ii)
C T=0
if
x=v and
^^<0 (^— >0)if M<0
dx
Proposition 4
of trade to
(M SO)
shows
that the
model predicts the
have a U-shaped form, with minimum
at
v
•
non-negative, the
for
all x.
dx
minimum
Volatility
.
D+E
graph
Since both
impose
If
D
is
in
terms
D and E
of this function is in the interval [0,v]. Empirically,
should expect most countries to have x<v, as the average country
median country
for the
lies well
one
above the
the world income distribution. Therefore, the theory does not
tight restrictions
on how a cross-section
small relative to E,
we would
of
terms of trade shocks would look.
expect most countries to be
in
the downward-
^To prove this, note first that VT and CT are identical to V and C as given in footnote 1 7, provided
we replace the growth rate sensitivities with the terms of trade sensitivities given in (28)-(31).
Performing
this substitution,
C =
we
find that
VT = y D
2
x + E (x - v)
•
•
M*E- v* x
t
are
.
,
V T -jo-[v-e a +(1-v)-e p
]
+«(»[v-K a
+(1-V)-Kp]
the derivatives of these expressions with respect to
x.
33
The
2
that
and
proposition then describes the signs of
sloping region of
in
V
T
.
If
D
we would
large relative to E,
is
the upward-sloping region of
V
T
Interestingly,
.
D and E can be
as a measure of the strength of the competition and
6-»°o, the competition bias
becomes
the cyclical bias disappears
shocks have small
cyclical biases.
a whole might not exhibit a strong
Proposition 4 also
upward-sloping
that,
cycle
if
in
countries,
and negatively
the cyclical bias
if
Alternatively,
offsetting,
M
i.e.
if
used
M<0. Since
quite large.
for the
T
C =0
the country as
if
terms of trade
x=v,
it
countries.
If
is
in
poor countries.
small for both shocks,
if
1
i.e.
If
M<0, the opposite
flat at
zero. Note that
£p->£a
and Kp—>Ka.
is true.
M
volatility
could
.
and comovement
of the growth
Figure 3 suggests that changes
2).
volatile in rich countries
more or
one
to
assume
(E»D)
in
we
the
poor ones, and that changes
in
that the theory
of Figure
show that M=0. These
that the cyclical biases are large
than
less equally correlated with the world cycle
is willing
is
in rich
approximately
3 as indicating that
E»D,
while the
restrictions are consistent with the notion
but go
in different
directions for different
shocks (M=0).
However,
this neither rules
out nor confirms whether the cyclical bias
important than the competition bias
On
the one hand,
the cyclical bias
is
one could
in
If
the cyclical biases of both shocks are large but
(See also Table
one could read the top panel
lower panel would
is
follows
terms of trade against the log-level of income for a subset of countries
the terms of trade are
correct,
if
£p»£a and Kp«Ka or £p«£a and KP »Ka
to construct Figure
and poor
ep»ea and Kp«Ka,
terms of trade be
for the
could be small even
terms of trade are less
in
necessary that both
is
it
Comovement graph
Turning to the data, Figure 3 plots the
rate of the
E->0
the terms of trade are positively correlated with the world
M=0, the Comovement graph
be zero
that the
biases respectively. As
cyclical
and yet E could be
cyclical bias
M>0 and downward-sloping
if
M>0, changes
in rich
shows
that, for
for instance,
If,
loosely interpreted
and D->0. As both £p-»£ a and Kp-*^,
irrelevant
and E->0. Note
expect most countries to be
is
more
shaping the cross-section of business cycles.
point to the condition that
E»D to support the view that
more important than the competition
34
bias.
On
the other hand,
one
could stress that
E»D does not necessarily mean that D
and use the condition M=0
the cyclical bias.
we
In
to
is
small
argue that the competition bias
is
any case, given our very crude measures
in
absolute value,
more important than
of the
terms of trade,
are reluctant to use Figure 3 to draw sharp conclusions regarding the relative
importance of our two hypotheses.
35
6.
Concluding Remarks
We
have developed two
alternative explanations of the
main features
of the
cross-section of business cycles. Both explanations rely on the observation that the
law of comparative advantage leads
rich countries to specialize in "high-tech"
products produced by skilled workers, while poor countries specialize
To
products produced by unskilled workers.
industries
respond
depend on the
properties
differently to
and poor
"low-tech"
the extent that "high-tech" and "low-tech"
domestic and foreign shocks, business cycles
industrial structure of
in rich
in
countries.
a country and, as a
We
result,
have
different
have focused on two such asymmetries: the
competition bias and the cyclical bias.
Our work suggests some
avenues
natural
On
for further research.
the
empirical front, the theory developed here provides a rich set of testable predictions
regarding the connection between the industrial structure of a country and the nature
business cycles that
of the
it
experiences.
To
investigate the empirical validity of
these predictions, one would have to
first
identify
domestic and foreign shocks. With
this
evidence
to
to quantify the extent to
trade
the theoretical front,
in financial
cycles. In the
it
is
in
an
natural to
models presented here, the
ask how the
price of
consumption.
integration to the
supplies
and
would then be possible
industry structure
possibility of cross-border
shape
of
consumption
an incentive
However, since neither factor supplies nor
affect
industries react
in different
dates and
for the establishment
market that redistributes consumption across dates and
consumption, a redistribution of the
would
in
it
how
instruments affects the shape of the cross-section of business
international financial
states.
hand,
in
the properties of business cycles.
states of nature varies across countries, creating
of
in
which cross-country differences
contribute to cross-country differences
On
asymmetries
If
latter
we want to
depend on
cannot affect output, although
it
certainly
construct an argument relating financial
a cross-section
their productivities to
their productivities
of business cycles,
consumption.
36
we need
One way achieve
to link factor
this is to
modify
preferences so as to introduce income effects on the labour supply.
preferred option would be to allow workers
technology, and then study
how
trade
and
firms to invest
in financial
investments, combines with commodity trade
business cycles.
37
in
In
in skills
our opinion, a
and
instruments, by affecting these
shaping the cross-section of
References
Acemoglu, D. and
C,
(1997)
"Was Prometheus Unbound by Chance?
Risk,
and Growth," Journal of Political Economy 1 05: 709-751
Diversification
Backus,
F. Zilibotti
P.
and Evidence"
Kehoe and Kydland
T.F.Cooley
in
(1995), "International Business Cycles: Theory
(ed.) Frontiers of
Business Cycle Research, Princeton
University Press.
and Business Cycles"
Baxter, M. (1995), "International Trade
Handbook of International Economics, Volume
K. Rogoff (eds.)
Christiano, L, M.
Corsetti,
G
Eichenbaum and C. Evans
Models
Participation
and
in
of
Money:
A
G.M. Grossman and
3,
(1997), "Sticky Price
North-Holland.
and Limited
Comparison", mimeo.
P. Pesenti (1998), "Welfare
and Macroeconomic Interdependence",
mimeo.
Davis, D. (1995), "Intraindustry Trade:
A
Heckscher-Ohlin-Ricardo Approach,"
Journal of International Economics 39: 201 -226
Harrison, J.M. (1990), Brownian Motion
Kraay,
A and
J.
and Stochastic Flow Systems,
Krieger.
Ventura (1997), "Trade and Fluctuations", mimeo.
Obstfeld and Rogoff (1995), "Exchange Rate Dynamics Redux," Journal of Political
Economy 103
Obstfeld, M.
(June):624-660.
and
K. Rogoff (1998), "Risk
and Exchange Rates", mimeo.
38
Figure
1:
Volatility
and Comovement
Volatility
0.16
0.14
0.12
0.1
§, 0.08 f
0.06
0.04
-
••
0.02
»
--
—I
6.5
7.5
8
(—
8.5
10
9.5
Iny
Comovement
0.8
T
0.6
"-
0.4
=g
0.2
-
--
9.5
10
-0.2
-0.4
Iny
top panel plots the standard deviation of the growth rate of real per capita GDP (dlny) over the period
1960-1994 against the log-level of average per capita GDP in 1985 PPP dollars over the same period (Iny),
for a sample of 88 countries. The bottom panel plots the correlation of real per capita GDP growth with
world average per capita GDP growth excluding the country in question (dlnY) over the period 1960-1994
agains the log-level of average per capita GDP over the same period. All data are at annual frequency.
The
consists of ell non-OPEC market economies with at least 30 observations on per capita income
beginning in 1960 in the Penn World Tables Version 5.6, extended to 1994 using constant price
local currency growth rates from the World Bank World Tables.
The sample
(RGDPCH)
Figure
2:
Sample Paths
of the Productivity Index
Country-Specific Variation Only
(o=0)
Time
Global Variation Only
(0 = 1)
Time
Both Country-Specific and Global Variation
(0<a<1)
Time
Figure 3: Volatility and
Terms
Comovement
of
of Trade
Volatility
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
Iny
Comovement
0.6
0.5
0.4
0.3
+
*-
0.2
-0.1
6\5
7.5
8.5
9.5
10
-0.2
-0.3
-0.4
Iny
The
top panel plots the standard deviation of the growth rate of terms of trade (dlnT) over the period
1
960-
1994 against the log-level of average per capita GDP in 1985 PPP dollars over the same period (Iny), for a
sample of 63 countries. The bottom panel plots the correlation of the growth rate of the terms of trade with
world average per capita GDP growth excluding the country in question (dlnY) over the period 1960-1994
agains the log-level of average per capita GDP over the same period. All data are at annual frequency.
Terms of trade growth is defined as the growth rate of the national accounts local currency export deflator
times the share of exports in GDP at constant local currency prices, less the growth rate of the
corresponding import deflator times the share of imports in GDP. The sample consists of all countries with
complete time series on these variables in the World Bank World Tables over the period 1 960-1 994. Five
countries for which terms of trade volatility was more than two standard deviations above the mean for all
countries were dropped from the sample (Argentina, Zambia, Israel, Bolivia and Nicaragua).
Table
1
:
Volatility
and Comovement
Comovement
Volatility
(Standard deviation of real
per capita GDP Growth)
Average
Correlation
(Correlation of real per
GDP growth with
world average excluding
country in question)
capita
Average
with ln(per
capita
Full
Sample
Correlation
with ln(per
GDP)
capita
GDP)
.051
-.621
.240
.627
.050
-.624
.264
.539
~*
*~
.259
.440
(88 countries, 1960-94)
Full
Sample, Non-Oil
Shock years
(88 countries, 1960-72,
1976-78, 1982-94)
Sample, using
unweighted world
average growth
Full
Sample, using
deviations from linear
trend instead of growth
.097
-.431
.525
.428
.031
-.573
.496
.425
.050
-.407
.260
.430
Third Quartile
.051
-.094
.140
.297
Bottom Quartile
.074
-.144
.066
.238
Full
rates
Top
Quartile
Second
Note:
by Income
Quartile
See notes
to Figure 1.
MIT LIBRARIES
3 9080 01444 0801
Table
and Comovement
the Terms of Trade
2: Volatility
of
Volatility
Comovement
(Standard deviation of terms
of trade growth)
(Correlation of terms of
trade growth with world
average excluding country
in
Average
Correlation
Average
with ln(per
capita
Full
Sample
question)
Correlation
with ln(per
GDP)
capita
GDP)
.054
-.420
.054
.095
.051
-.416
.044
-.257
.072
.338
(84 countries, 1960-92)
Full
Sample, Non-Oil
Shock years
(84 countries, 1960-72,
1976-78, 1982-92)
Sample, using
unweighted world
average growth
Full
Sample, using
.066
.387
.211
-.330
.015
-.153
.072
-.563
.068
-.299
.074
.202
Third Quartile
.069
.238
.053
-.263
Bottom Quartile
.074
-.048
.006
.038
Full
deviations from linear
trend instead of growth
rates*
Top
Quartile by
Second
Income
Quartile
See notes to Figure 3.
For this row only, the level of the terms of trade is defined as a geometric average of the import and
export deflators, using the export and import shares in GDP as weights.
Note:
*
-
/,
g 7
:
Date Due
Lib-26-67