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DEWEY
\4f
1
Technology
Department of Economics
Working Paper Series
Massachusetts
Institute of
Comparative Advantage and the
Cross-Section ot Business Cycles
Aart Kraay, The World Bank
Jaume Ventura, MIT
Working Paper 98-09Revised
January 2001
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssrn.com/paper.taf7abstract id-=1 371 75
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
OCT l
6 2001
LIBRARIES
*\
Technology
Department of Economics
Working Paper Series
Massachusetts
Institute of
Comparative Advantage and the
Cross-Section of Business Cycles
Aart Kraay, The World Bank
Jaume Ventura, MIT
Working Paper 98-09Revised
January 2001
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssrn.com/paper.taf7abstract id-=1 371 75
Comparative Advantage
and the
Cross-section of Business Cycles
Aart Kraay
Jaume Ventura
The World Bank
M.I.T.
December 2000
Business cycles are both less volatile and more synchronized with the
world cycle in rich countries than in poor ones.
develop two alternative
explanations based on the idea that comparative advantage causes rich countries to
Abstract
:
We
specialize
in
industries that
use new technologies operated by skilled workers, while
industries that use traditional technologies operated by
poor countries specialize in
unskilled workers. Since new technologies are difficult to imitate, the industries of rich
countries enjoy more market power and face more inelastic product demands than
those of poor countries. Since skilled workers are less likely to exit employment as a
result of changes in economic conditions, industries in rich countries face more
inelastic labour supplies than those of poor countries. We show that either
asymmetry in industry characteristics can generate cross-country differences in
business cycles that resemble those we observe in the data.
We are grateful to Daron Acemoglu and
Fabrizio Perri for useful comments.
are the authors' and do not necessarily reflect those of The World Bank.
The views expressed here
,
Business cycles are not the
is
in
the top panel of Figure
income growth against the
countries.
We
we
,
level of (log)
downwards. A second difference
bottom panel
1
refer to this relationship
more synchronized
1
we
,
and poor countries. A
is
plot the
is
in rich
countries than
countries and years.
Why
cycle
in rich
more
in
poor ones? Part
political
and
same
in
In
the
question,
set of countries.
it
We refer to
slopes upwards. Table
of the
1
sub-samples
of
to the production of agricultural
minerals. Table
shows
fraction of the variation
in
the
of the variation in the
a
answer must be
with the world
that poor
open or more
and they also have a higher share
economy devoted
that, in
more synchronized
policy instability, they are less
distant from the geographical center,
much
slopes
1
countries than
1
poor ones.
that these facts apply within different
are business cycles less volatile and
countries exhibit
in
it
income growth are
income growth, excluding the country
shows
in
per capita income growth rates
as the comovement graph and note that
self-explanatory,
countries than
graph and note that
that fluctuations in per capita
against the level of (log) per capita income for the
which
difference
standard deviation of per capita
volatility
plot the correlation of
with world average per capita
this relationship
in rich
first
per capita income for a large sample of
as the
with the world cycle
of Figure
in rich
income growth are smaller
that fluctuations in per capita
poor ones,
same
statistical
volatility of
comovement
of their
products and the extraction of
sense, these factors explain a substantial
income growth, although they do not explain
of
income growth. More important
for
our
purposes, the strong relationship between income and the properties of business
cycles reported
in
Table
1
is still
present after
we
control for these variables. In short,
there must be other factors behind the strong patterns depicted
differences
in political instability,
in
remoteness and the importance
Figure
1
beyond
of natural
resources.
With the exception that the comovement graph seems to be driven by differences between rich and
poor countries and not within each group. Acemoglu and Zilibotti (1997) also present the volatility graph.
They provide an explanation for it based on the observation that rich countries have more diversified
production structures.
We
are unaware of any previous reference to the
comovement graph.
.
In this
why business
countries than
paper,
we develop two
cycles are less volatile and
more synchronized
poor ones. Both explanations
in
advantage causes
rich
non-competing explanations
alternative but
countries to specialize
rely
with the world
on the idea
that
in rich
comparative
new
industries that require
in
for
technologies operated by skilled workers, while poor countries specialize
in
industries
that require traditional technologies operated by unskilled workers. This pattern of
specialization
opens up the
business
possibility that cross-country differences in
cycles are the result of asymmetries between these types of industries.
In particular,
both of the explanations advanced here predict that industries that use traditional
technologies operated by unskilled workers
shocks. Ceteris paribus, these industries
will
will
be more sensitive
not only be
more
to country-specific
volatile but also less
synchronized with the world cycle since the relative importance of global shocks
To
lower.
is
the extent that the business cycles of countries reflect those of their
industries, differences in industrial structure could potentially explain the patterns in
Figure
1
One
explanation of
idea that firms using
why
industries react differently to shocks
new technologies face more
those using traditional technologies.
for technical
New
inelastic product
technologies are
reasons and also because of
them monopoly power
imitate
in
based on the
demands
difficult to imitate
than
quickly
legal patents. This difficulty confers a cost
advantage on technological leaders that shelters them from
gives
is
potential entrants
and
world markets. Traditional technologies are easier to
because enough time has passed since
their
adoption and also because
patents have expired or have been circumvented. This implies that incumbent firms
face tough competition from potential entrants and enjoy
in
little
or no
monopoly power
world markets.
The
price-elasticity of
product
demand
affects
how
industries react to shocks.
Consider, for instance, the effects of country-specific shocks that encourage
production
in all
industries. In industries that
monopoly power and face
fluctuations
in
inelastic
demands
use new technologies, firms have
for their products.
supply lead to opposing changes
industry income. In industries that
use
in
As a
result,
prices that tend to stabilize
traditional technologies, firms
face
stiff
demands
competition from abroad and therefore face elastic
supply have
result, fluctuations in
is
more
volatile.
competition
be
is
To the
little
extent that this
important,
incomes
or
no
effect
asymmetry
on
in
of industries that
less sensitive to country-specific
for their products.
their prices
As a
and industry income
the degree of product-market
use new technologies are
shocks than those
likely to
use
of industries that
traditional technologies.
Another explanation for why industries react differently to shocks
the idea that the supply of unskilled workers
workers.
more
A
first
reason for
attractive to unskilled
ones. Changes
labour
in
abandon the labour
workers.
is
this
A second
employment
The
is
that
elastic than the supply of skilled
non-market
workers whose market wage
demand
might induce
reason for the asymmetry
in
more
some
is
activities
are relatively
lower than that of skilled
unskilled workers to enter or
in
minimum wage. Changes
and out
of skilled
labour supply across
in
labour
demand
unemployment, but are not
of
might force
likely to affect
in all
of unskilled
is elastic,
workers.
in
on the employment
how
industries that
asymmetry
in
and
shocks than those
that
is inelastic,
make
the
industry
of industries that
use
To study these hypotheses we
demand. Since
industry
likely to
skilled
is
is
in
supply
in
income more
same shocks have
income
the elasticity of labour supply
use unskilled workers are
shocks that
use them, fluctuations
of skilled workers. In industries that
fluctuations in supply are not magnified
extent that this
raise the labour
employment
Since the supply of skilled workers
effects
the
these shocks lead to large fluctuations
In industries that
are therefore magnified by increases
no
and therefore
industries
the supply of unskilled workers
volatile.
some
workers.
industries react to shocks. Consider again the effects of country-specific
encourage production
categories
skill
wage-elasticity of the labour supply also has implications for
employment
based on
force, but are not likely to affect the participation of skilled
the imposition of a
unskilled workers
asymmetry
is
is
little
or
use them,
less volatile.
To
the
important, incomes of
be more sensitive
to country-specific
workers
construct a stylized world equilibrium model of
the cross-section of business cycles. Inspired by the work of Davis (1995),
we
consider
in
section
one a world
which differences
in
Heckscher-Ohlin and industry technologies a
la
in
both factor endowments a
Ricardo combine to determine a
country's comparative advantage and, therefore, the patterns of specialization
trade.
To generate business
productivity fluctuations that
In
we
section two,
asymmetries
in
we
economy
in
to the sort of
Figure
calibrate the
1
demand
seems
to
respectively;
Using available microeconomic estimates of the key
.
model and
and
We explore these
we
(ii)
find that:
(i)
The asymmetry
The model
in
exhibits slightly less
on the slopes
elasticity in the
labour supply.
results further
in
variation in
monetary policy and
business cycles.
model
Once these
exhibits roughly the
percent of the variation
in
of the volatility
sections three and four.
extend the model to allow for monetary shocks that have
face cash-in-advance constraints.
in volatility
the elasticity of product
effect
have a quantitatively stronger
comovement graphs, than the
show how
and/or labour supply can be used to
than two-thirds and one-third of the observed cross-country variation
comovement,
and
have been emphasized by Kydland and Prescott (1982). 2
the elasticity of product
we
subject this world
characterize the cross-section of business cycles and
explain the evidence
parameters,
cycles,
la
In
and
demand
and
section three,
real effects since firms
We use the model to study how cross-country
financial
development
affect the cross-section of
factors are considered, the calibrated version of the
same
cross-country variation
comovement as
the data.
In
in volatility
section four,
and about 40
we show that the
two industry asymmetries emphasized here lead to quite different implications for the
cyclical
behavior of the terms of trade.
data, the picture that
appears
Namely, the asymmetry
important than the
2
in
is
clear
When we
confront these implications with the
and confirms our
earlier calibration result.
the product-demand elasticity
asymmetry
in
seems
quantitatively
more
the labour-supply elasticity.
open-economy real business cycle models that
shocks are transmitted across countries. See Baxter (1995) and Backus,
Kehoe and Kydland (1995) for two alternative surveys of this research. We differ from this literature in
two respects. Instead of emphasizing the aspects in which business cycles are similar across countries,
we focus on those aspects in which they are different. Instead of focusing primarily on the implications
of international lending, risk sharing and factor movements for the transmission of business cycles, we
emphasize the role of commodity trade.
Our research
studies
how
is
related to the large literature on
productivity
The main theme
of this
paper
is
that the properties of business cycles differ
across countries because they have different industrial structures. There are
determinants of the industrial structure of a country.
most important
we
five
of
such determinants,
of business cycles.
"iceberg" transport costs
reductions
industrial structure
If
and the cross-section
One should
different
In this
in
in
into
of the
business cycles that
of
business cycles
is flat.
in
production.
As a
As
transport costs
result, industrial structures
of Trade
section,
we
and Business Cycles
present a stylized model of the world economy. Countries
skilled
workers are
objective
is
to
cross-country variation
cross-country variation
income
of a country also
is,
the
determine
to
same
its
industrial
develop a formal framework that allows us to think about
in industrial
in
structure,
and therefore income, translates
the properties of the business cycle.
We consider a world with a continuum
good and two continuums
and also tend
richer,
industries that use these factors intensively. That
Our
same
countries have the
all
therefore expect globalization to lead to business cycles that are
characteristics that determine the
structure.
(modeled here as parametric
which a country has comparative advantage
have better technologies and more
specialize
how
section
across countries.
A Model
that
ability to trade. In
transport costs are high enough,
increase and so does their share
diverge.
globalization
changes the nature
decline, the prices of products
.
a country's
We introduce trade frictions in the form of
and study how
transport costs)
in
countries experience.
1
is,
perhaps the
explore further the connection between international trade, industrial structure
and the nature
more
that
We focus here on
many
of intermediates
mass
of countries with
indexed by ze[0,1], which
one; one
we
final
refer to
as
the a- and (3-industries; and two factors of production, skilled and unskilled workers.
There
is
free trade
emphasize the
in
role of
intermediates, but
commodity
trade,
we do
we
not allow trade
in
the
final
good. To
rule out trade in financial instruments.
To
problem
simplify the
further,
we
also rule out investment. Jointly, these assumptions
imply that countries do not save.
Countries
differ in their
and
unskilled workers
by a
country
is,
5
is
\i
is
a measure
the fraction of the population that
technology are stable, so that
in
time-invariant joint distribution.
productivity index
n
level of skills
and
consumers by
ie [1 ,»)
following expected
and
Ejufc(i)
\i
and 5 are constant.
the value of non-market
and assume
=1-i _x
F(i)
that this index
with X>0.
,
is
is
be
Let F((i,5)
their
who
differ in their
activities.
We
wage.
We
index
distributed according to this
A consumer
with index
i
maximizes the
utility:
WVe-.dt
utility
function;
c(i) is
an indicator function that takes value
r(|i,5,7i)
(H,5,7t)-country.
skilled
of
We generate business cycles by allowing the
wage as
any well-behaved
otherwise. Let
constraint
an index
is
';
v
U(.) is
l(i) is
and n
their personal opportunity cost of work, or reservation
Pareto distribution:
where
defined
is
the technology of the
populated by a continuum of consumers
is
think of this reservation
o
is skilled,
each country
to fluctuate randomly.
Each country
(1)
how advanced
of
and
of skilled
We assume that workers cannot migrate and that cross-country
productivity.
differences
endowments
their level of productivity. In particular,
where
triplet (n,5,7t),
technologies, their
and
w(fx,8,7t)
1
if
be the wages
consumption
the
simply p F
•
c(i)
=
w
•
l(i)
for unskilled
good
consumer works and
of skilled
Also define p F (n,8,7t) as the price of the
of the final
and
final
unskilled workers
in
a
good. The budget
workers and p F
•
c(i)
=
r
•
l(i)
for
ones.
The consumer works
unskilled)
if
and only
exceeds a reservation wage
if
the applicable real
1
of
i"
8
.
Let
s(u.,5,7t)
and
wage
(skilled or
u(n,5,Tt)
be the measure
of skilled
and
Under the assumption
unskilled workers that are employed.
and reservation wages are independent, we have
distribution of skills
f
-
that the
that
\
if
r
< pF
if
r
> pF
vPf,
(2)
(1-5)
u
(3)
=
'w^
1-5
If
if
w
< pF
if
w
> pF
K^J
\
wage
the real
of
any type
of
worker
is
supply of this type exhibits a wage-elasticity of
dispersion of reservation wages.
If
the entire labour force of this type
This elasticity depends only on the
X.
wage
the real
is
less than one, the aggregate labour
of
any type
of
worker reaches one,
employed and the aggregate labour supply
this
type of workers
becomes
real
wage
workers exceeds one,
vertical.
Throughout,
—>
we
consider equilibria
x
for skilled
1
,
wage
while the real
in
for
which the
for unskilled
Pf
workers
is
less than one,
—w <
1
.
That
is, all
countries operate
in
the vertical region
Pf
of their supply of skilled
workers and the elastic region of
workers. This assumption generates an asymmetry
aggregate labour supply across
workers and X>0
for unskilled
skill
ones.
in
As X-^0,
this
This
combine intermediates
is
the case
countries,
i.e.
in
5«1.
equilibrium
if
to
produce the
skilled (unskilled)
final
supply of unskilled
the wage-elasticity of the
categories. This elasticity
is
zero for skilled
asymmetry disappears.
Each country contains many competitive firms
firms
their
in
the
final
good according
workers are
sufficiently
goods
sector.
These
to this cost function:
scarce (abundant)
in all
.
V
"1
1-e
JPa(zr dz
B(p a (z),p p (z)) =
(4)
1-v
"1
M)
1
Jp P
_0
The
between
between any two
in
for the final product
industries
varieties within
some workers
Since there are always
demand
-e
is
is
one, while the elasticity of
an industry
is 9,
with 6>1
that participate in the labour force, the
always strong enough
Our assumptions on technology imply
equilibrium.
dz
.0
elasticity of substitution
substitution
(z)
to
generate positive production
that firms in the final
good
sector spend a fraction v of their revenues on a-products and a fraction 1-v on
products. Moreover, the ratio of spending on any two a-products z and
z' is
(3-
given by
1-e
1-e
Pa(z)
;
and the
spending on any two (3-products z and
ratio of
Pp(z)
z' is
P.(z')
Pp(z')
where p a (z) and p
(z)
denote the price
respectively. Define P n
and P p as the
of variety z of the a-
and
(3-products,
ideal price indices for the a-
and
(3-industry,
i.e.
1
1-e
Pa =
1
Jp a
(z)
numeraire
1
and PR =
-dz
1
Jp p
(z)
-e
-dz
;
and define the following
rule:
v
(5)
-9
= P«
-Pp"
v
Since firms
in
the
final
goods sector are competitive, they set
price equals
cost. This implies that:
(6)
p F =1
Since
of the final
all
good
intermediates are traded and the law of one price applies, the price
is
the
same
in all
countries. In this world
10
economy, purchasing
power
is
parity applies.
not traded
is
An
implication of this
that the
is
assumption that the
industries.
The
sophisticated production processes that require skilled workers.
a different technology that
is
owned by one
variety of a-products, the firm that
As mentioned, the
owns
firm only.
owned by a domestic
advanced the technology
We can
of a country
technology and market structure
demand
for
any variety
of
in
the
a-product
It
unit of
any
in
is
not under
which the technology
n as a natural indicator
of
how
follows from our assumptions on the
final
is 0.
variety requires
n fluctuates randomly and
interpret
is.
Each
the technology requires e" units of skilled
productivity index
firm.
a-industry uses
To produce one
the control of the firms. Let n be the measure of a-products
is
good
not binding.
Each country also contains two intermediate
labour.
final
goods sector
As a
that the elasticity of
result, all firms in
the a-industry face
downward-sloping demand curves and behave monopolistically. Their optimal pricing
policy
is
a markup over unit cost. Let pjz) be the price of the variety z of the a-
to set
industry.
Symmetry ensures
all
the firms located
in
a
(|i,8,7i)-country set the
same
price for their varieties of a-products, p a (ja,8,7r):
pa =
(7)
As
re"
6-1
usual, the
The
markup depends on the
(3-industry
uses
elasticity of
traditional technologies that
demand
for their products.
are available to
countries and can be operated by both skilled and unskilled workers.
unit of
any variety
have assumed
of (3-products firms require
that
in
equilibrium skilled
the
same
technologies, they
competitively.
They
all
face
flat
all
firms
individual
set price equal to cost. Let p
11
firms
in all
To produce one
e " units of labour of any kind. Since
wages exceed
unskilled workers produce (3-products. Since
all
in
unskilled
wages, only
the (3-industry have access to
demand curves and behave
(z)
we
be the price of the variety z
of
the (3-industry.
Symmetry ensures
set the
same
(8)
p p =w-.e-"
With
all
firms
the P-industry of a (n,5,7r.)-country
in
varieties of (3-products, p^n,S,n):
this formulation,
this
;
all
demand. This
of product
As 0^co
price for
that
we have
elasticity is
introduced an asymmetry
in
the a-industry and
the price-elasticity
infinity in
productivity shocks.
The index %
component,
We
n-Y\.
Each
is
of
the
sum
of
refer to
changes
these components
2
instantaneous variance equal to r\a and
on
and assume
[-n,7i]
characteristics.
this distribution is
Under the assumption
components are independent across
distribution of 71-n is
time invariant.
has been defined as an index
average
productivity.
The instantaneous
is
therefore Jr)
variation in
whether
it
5
.
(1-r|)rj
4
that
is
an independent Brownian
domestic productivity
See Harrison
This
is
and
% >0, 0<r|<1 and
distributed
in
these country-specific
we have
that the cross-sectional
refer to this distribution
regulates the
n
as G(7i-n). While n
serves as an index of world
volatility of
the domestic shocks.
between domestic shocks, dn, and foreign shocks, dn,
The parameter
comes from dn
drift
components be uniformly
domestic productivity,
of
The parameter a
correlation
respectively, with
changes
countries,
We
n as
independent of other country
ti
is
therefore regulates the extent to which the
due
to global or country-specific
or d(7i-n). Figure 2
under three alternative assumptions regarding
4
2
distribution of country-specific
initial
in
a global component, n, and a country-
motion reflected on the interval [-1,1] with changes that have zero
a>0. Let the
the (3-industry.
asymmetry disappears.
Business cycles arise as n fluctuates randomly.
specific
in
components,
shows possible sample paths
of
i.e.
n
t|.
(1990), Chapter 5.
true except
when
either
n or
n
are at their respective boundaries. These are rare events since
the dates at which they occur constitute a set of
measure zero
12
in
the time
line.
A
competitive equilibrium of the world
and quantities such
prices
In
world
the a-industry, different products
demands
country,
for the
— P.W
(sum
,
of
must equal the
and
is
unique.
command
different prices.
The
ratio of
supplies
ratio of
se'
is
.
(n',d',n')-
Using
this
se
and the
condition plus Equation (2)
1
va
and markets
a-products of a (^,5,7i)-country and a
all)
of
prices.
Pa(z')
Pa
optimally
that a competitive equilibrium exists
We prove this by constructing the set of equilibrium
sequence
consists of a
consumers and firms behave
that
Our assumptions ensure
clear.
economy
definition of
Pa
we
find that:
n-n
H ^9
(9)
=
*¥„
IW
—
e-1
1
where
8
(n-n)
9
dF-dG
and G(n-n) are
its
time-invariant,
own
¥a
x
a constant. Since each country
is
many
skilled
with relatively high productivity (high 7i-n) producing a small
produce large quantities
prices.
As
In
is
a "large"
depends
varieties of a-products, the price of these varieties
negatively on the quantity produced. Countries with
|i)
F(u.,8)
J
v.
producer of
Since the distribution functions
of
each
the (5-industry
varieties of (3-products
all
products
command
in
Equation
(4).
Pp
(10)
13
8)
of varieties (low
and as a
result,
disappears and p (z)—>p a
face low
.
ra
the
would not be produced. But
given the technology described
number
variety of the a-products
9^>°°, the dispersion in their prices
workers (high
same
price. Otherwise, low-price
this is not
Therefore,
it
a possible equilibrium
follows that:
n
Finally,
we compute
the ratio of world spending
the relative price of both industries.
in
To do
equate
this,
v
the a- and (3-industries,
,
to the ratio of the value
1-v
s-e"dFdG
ffp a
^jPpue
of their productions,
.
n
Using Equations
(2)-(3)
and
dFdG
(5)-(10),
we
j
then find that:
\~
1
v
%
1-v
Wn
f
(11)
P
where
yp
—-—
1+X.-V
1+Xv
•e*
= JJ(1-5)-e (1+X)(n_n)
dFdG
,
and
is
constant.
If
X>0, high productivity
is
associated with high relative prices for a-products as the world supply of (3-products
is
high relative to that of a-products. This increase
is
due
to increases in
employment
of unskilled
in
the relative supply of (3-products
workers. As A.-^0, the relative prices of
both industries are unaffected by the level of productivity.
What
be the income and the share
x(n,5,Tr)
y =
are the patterns of trade
\
/
(p a s
•
+ p p u} e" and x =
•
d
—
technologies (high n) and more
and
x.
We therefore
them
in
s o
v,
respectively.
and
i.e.
71
.
Not surprisingly, countries with better
capital (high 5)
number
goods,
all
production of a-products and import almost
final
Let y(n,§,7i)
•
human
final
economy?
of the a-industry in a (n,5,7i)-country,
infinitesimal
the production of
production of
world
refer to countries with high
each country produces an
of
•
in this
have high values
values of x as
of varieties of
y
Since
rich countries.
a-products and uses
countries export almost
all
for both
of the a-products
all
used
all
of their
in
the domestic
goods. As a share of income, these exports and imports are x and
To balance
their trade, countries with
countries with x>v import them.
As a share
of
14
x<v export (3-products and
income, these exports and imports are
v-x
and
x-v, respectively. Therefore,
usual, this trade
can be decomposed
interindustry trade,
x-v
I
The
factor proportions.
proportions. The
the share of trade
|
.
The former
consists of trade
and
in
2.
trade
among poor
The Cross-section
In
to the
in
little
and
a stylized manner three broad empirical
a large volume of intraindustry trade
between
rich
and poor
countries.
Business Cycles
economy described
the world
same
of
As
products with different factor
later consists of trade in
model therefore captures
(c)
max[v,x].
products that have similar
in
rich countries, (b) substantial interindustry trade
countries,
is
into intraindustry trade, min[v,x],
regularities regarding the patterns of trade: (a)
among
income
in
in
the previous section, countries are subject
Any
type of country-specific and global shocks to productivity.
difference
the properties of their business cycles must be ultimately attributed to differences
in their
technology and factor proportions. This
is
clearly a simplification. In the real
world countries experience different types of shocks and also differ
beyond technology and factor proportions. With
ask:
How much
potentially
The
first
answer
is
to the
between one and two
of
a
mind,
thirds of
is
ways
in this
(n.,5,7t)-country
as a
1),
linear
we
dlny-E[dlny] =
x-
—
section
all
we
the variation.
to obtain
an expression
obtain the
Ito's
that
lemma
(demeaned) growth
combination of country-specific and
1
+ (1-x)-(1 + X)
d(7t-n)+
+x
1+X-v
15
go
Perhaps
global shocks:
(12)
that
business cycles could
shocks that countries experience. Applying
the definition of y and using Equations (2)-(1
income
in
in
of the previous section?
step towards answering this question
income growth
rate of
caveat
observed cross-country variation
be explained by the simple model
surprisingly, the
links
of the
this
in
dn
to
Equation (12) provides a complete characterization of the business cycles
experienced by a
measured by
(u.,5,7i)-country
as a function
as
of the country's industrial structure,
Equation (12) shows that poor countries are more sensitive to
x.
3dlny
country-specific shocks,
is
i.e.
decreasing
in x.
Equation (12) also
ad(Ti-n) dn=o
shows
that
all
countries are equally sensitive to global shocks,
x.
Why are
We next discuss the intuition
poor countries more sensitive
X-^0 and 9^°° so that the a-and
>
specific increase
in
productivity
to country-specific
=
1
if
In this
case, a one percent country-
has no effects on employment or product
and 6^^.
A.-^0
shocks? Assume
(3-industry face both perfectly inelastic factor
production and income also increase by one percent. This
3dlny
d(;t-n)=o
behind these results.
supplies and perfectly elastic product demands.
result,
is
adn
independent of
that
i.e
positive,
is
If A,
is
prices.
As a
why
a country-specific increase
in
ad(Ti-n) dn=o
productivity of
one percent leads
an increase
to
industry and, as a result, production
in
employment
of
A.
percent
in
the
(3-
and income increase by more than one percent.
This employment response magnifies the expansionary effects of increased
productivity
in
the (3-industry.
3dlny
countries,
As a
=
i.e.
1
+
result,
(1
—
x)
-
the shock has stronger effects
A,
if
8—>°°.
If
6
is finite,
in
poor
a country-specific
3d(7t-n) dn=o
increase
in
productivity of
one percent leads
to
a
0" 1
percent decrease
in
prices
in
the
a-industries. This price response counteracts the expansionary effects of increased
productivity
in
the a-industry. Consequently, the shock has weaker effects
Bdlny
countries,
=
i.e.
—
x
1
if
X=0.
If
X>0 and 9
the employment and price responses combine to
country-specific shocks,
=x
i.e.
dd(Ti-n)
dn=o
16
is finite,
make poor
—1
9
+ (1 -
x)
we have
in rich
that both
countries react
(1
+ X)
is
more
decreasing
to
in x.
Why are
all
on the assumption
countries equally responsive to global shocks? This result rests
that the elasticity of substitution
one. Consider a global increase
in productivity.
On
between a- and (3-products
the
one hand, production
is
of p-
products expands relative to the production of a-products as more unskilled workers
are employed. Ceteris paribus, this would increase the share of world income that
goes
and hence poor
to the p-industry,
the increase
in relative
countries, after a positive global shock. But
supply lowers the relative price of p-products. This reduces
the share of world income that goes to the P-industry, and hence poor countries, after
a positive global shock. The assumption of a Cobb-Douglas technology
production of the
world spending
in
in
final
good implies
two effects cancel and the share
of
the a- and P-industries remains constant over the cycle. Therefore,
our framework differences
in industrial
countries react to global shocks.
We are ready to use the
from Equation (12)
structure
do not generate differences
in
how
6
model
dlnY as the world average growth
to interpret the
rate, i.e.
evidence
dlnY = jj dlny
in
dFdG
Figure
.
1
Then,
Define
.
it
follows
that:
1
dlnY-E[dlnY] =
(13)
that these
for the
1
+X
dn
+ A-v
Since the law of large numbers eliminates the country-specific component of
shocks
in
the aggregate, the world
countries that belong to
6
economy
exhibits milder cycles that
any
of the
7
it.
is special, it is not difficult to grasp what would happen if we
the elasticity of substitution between industries were higher than one, poor countries would
While the Cobb-Douglas formulation
relaxed
it.
If
be more sensitive
shocks than
as the share of world income that goes to the |3and decreases after a negative one. If the elasticity of
substitution were less than one, the opposite would be true.
7
Once again, this result rests on the Cobb-Douglas assumption. If the elasticity of substitution between
a- and |3-products were higher than one, the very rich countries might exhibit business cycles that are
to global
rich countries
industry increases after a positive global shock
milder than those of the world.
17
Let V(n,8,7i) denote the standard deviation of
country, and
let CQx,5,7c)
denote the correlation
of
its
income growth
we find
shocks,
in
Figure
1
(14)
x
o-.
^+x
'
.^I + (1-x)-(1 + X)
C=
1
x
(1"T1)
+
+ 1-v
.®^ + (1-x)-(1 + X)
Figure 3 plots the
parameter values. Except
volatility
graph
downward
intuition is clear:
As a
1
+
•(1-71)
(3-industry.
This
makes
in
sloping
+A
+ X-v
the limiting case
Tl
is
in
of x, for
where both X=0 and
and the comovement graph
asymmetries
result of
and labour supply, the a-industry
+ X-v
and comovement graphs as functions
volatility
different
is
^
f\
1
The
and
to the volatility
that:
-\
(15)
(u.,5,7t)-
Using Equations (12)-(13) and the properties of the
.
-i2
V=
a
income growth with world
average income growth. These are the theoretical analogs
comovement graphs
of
is
upward
0=<~, the
sloping.
the elasticity of product-demand
less sensitive to country-specific
the a-industry less volatile and
shocks than the
more synchronized
with the
world cycle than the (3-industry. Since countries inherit the cyclical properties of their
industries, the
incomes
of rich countries are also less volatile
with the world cycle than those of poor countries.
is
and more synchronized
The magnitude
of
these differences
more pronounced as X increases and/or 6 decreases.
A
simple inspection of Equations (14) and (15) reveals that there exist various
combinations of parameters capable of generating approximately the data patterns
displayed
in
Figure
1
and Table
1
.
In this
evidence that motivated the paper. But
impose more
values that
range
for x.
discipline
seem
by
sense, the model
this is
With these choices
at
this,
hand,
we
we
18
able to replicate the
a very undemanding
restricting the analysis to
reasonable. To do
is
combinations
criterion.
of
One can
parameter
next choose values for a,
r\,
v and a
then examine how the cross-section of
business cycles varies with X and
Needless
9.
strong conclusions from a calibration exercise
As noted above,
also differ
that
and
of countries
industries,
the large cross-section of countries
To determine
The model
Since
this
share
so that caution
we
in
around 60 percent
bound
The model
for x.
poor countries, and that
GDP
is
around 20 percent
0.1
in
x,
we use
income
the richest countries
in
in
choose v=0.2 and use
generalizing to
in
in
in
countries
our sample,
also predicts that v
is
for x.
The choice
in
problem by choosing a and
and comovement
of
8
parameters. This
model's
ability to
comovement
The
of
income growth
means
capita
of
volatility
rj
and
r\
around
6.5),
In particular,
choices
for
more
We
level of volatility
for the typical rich country, given the rest of our
can only
tell
us about the
in volatility
and
panel of Table 2 reports the results of this calibration exercise,
in
Figure
3.
The
around 9.5) and the poorest country
a and
r|
row reports the predicted
first
and comovement between the
based on the regressions
A and
is
we
income growth.
in volatility
of
the share of
and cross-country
match the observed
match observed cross-country differences
top-left
GDP
to
that this calibration exercise
and selected cases are shown
difference
r|
we use
our sample,
correlation of productivity growth for this large cross-section of countries.
this
is x.
these countries x<v. Since the share
problematic, since there are no reliable estimates of the
circumvent
shall
data on trade
in rich
the poorest countries
as a lower bound
we
this exercise.
predicts that the share of exports
is
when
order
study here. Despite these caveats,
income
of exports in
is in
the relevant range of variation for
0.6 as a reasonable upper
exports
factor proportions. Moreover,
X and 9 are based on non-representative
see that some useful insights can be gained from
shares.
draw
a model as stylized as ours.
like this in
go beyond technology and
available estimates of the key parameters
samples
to
the real world countries experience different types of shocks and
in
ways
in
one should be cautious
to say,
with controls
richest country (with log per
(with log per capita
in
Table
1
.
GDP
of
The remaining rows
are chosen to ensure that V=0.04 and C=0.4, for x=0.5, v=0.2 and the given
9.
19
report the difference
poorest (x=0.1
)
in volatility
and comovement between the
countries that the model predicts for different values of X
These values encompass
existing
and
richest (x=0.6)
and
0.
microeconomic estimates. Available industry
estimates of the elasticity of export
demand range from 2
10 (see Trefler and Lai
to
(1999), Feenstra, (1994)), while available estimates for the labour supply elasticity of
unskilled workers range from 0.3 to 0.35
table also reports the values for
Table 2 shows
can account
rich
that,
a and
r\
(See Juhn, Murphy and Topel (1991)). The
that result from the calibration procedure.
using values for 8 and X of 9=2 and A.=0.35, the model
between
for nearly two-thirds of the cross-country difference in volatility
and poor countries (-0.016 versus
cross-country differences
in
-0.026),
and
slightly less
comovement (0.129 versus
than one-third of the
0.382).
These values
for the
parameters are within the range suggested by existing microeconomic studies.
industry asymmetries are
predicted differences
These
values.
results
assumed
in volatility
to
be even stronger, say 9=1
and comovement are closer
such a
stylized
model as ours. Moreover, we
shall
see
in
in
the
and X=0.7, the
to their predicted
seem encouraging. The two hypotheses
account for a sizeable fraction of cross-country differences
.2
If
put forward here can
business cycles even
in
the next section that a
simple extension of the model that allows for monetary shocks and cross-country
differences
in
the degree of financial development can
move
the theoretical
predictions closer to the data.
A second
demand seems
result in
Table 2
quantitatively
is
that the
asymmetry
in
the elasticity of product
more important than the asymmetry
in
the labour supply. Within the range of parameter values considered
changes
to
have
in
is
in
Table
2,
9 have strong effects on the slope of the two graphs, while changes
little
consider
the elasticity of
or no effect.
To
the extent that this range of parameter values
in
we
the relevant one, this calibration exercise suggests that the asymmetry
asymmetries
hypothesis of
in
the elasticity of product
why business
point in section four
demands
constitutes the
cycles are different across countries.
where we attempt
to distinguish
examining terms of trade data.
20
more promising
We
X
return to this
between hypotheses by
in
3.
Monetary Shocks and Financial Development
Our simple
account
for
calibration exercise tells
almost two-thirds of the cross-country differences
one-third of the cross-country variation
model
that the
is
surely too stylized to
made
our modelling choices were
model
fit.
Now
that the
by adding
to
in
comovement. One
it
is
maximize
reaction to this finding
and cross-country
we choose
this
extension highlights are both
narrow
this
gap, but
variation
in
to follow this route
and
realistic
We now allow countries to differ also
and
their
monetary
where k
(|j.,5,7:,k,i),
interest rate
policy.
is
Each country
is
interesting
in their
financial
constraint.
9
In particular, firms
a fraction k of
therefore
we
We assume that k
wage
bill
limit in
Christiano,
i
development
is
not the only
in their
own
have
to
right.
of financial
is
development
\i,
that firms face a cash-in-advance
credit markets.
which credit markets are so
efficient that
As
.
in
order to pay
The parameter k
k^O
cash
is
a discussion of related models.
21
the
We allow for an
8 and k.
before production starts, with 0<k<1
for
i is
constant over time and re-
use cash or domestic currency
Eichenbaum and Evans (1997)
that
fluctuate randomly.
money by assuming
measures how underdeveloped are
reach the
See
their
that by
therefore defined by a quintuplet,
additional source of business cycles by letting
motivate the use of
of
closer to
a measure of the degree of financial development, and
on domestic currency.
is
intuitions
because the elements
degree
define F(^,5,k) as the time-invariant joint distribution of
We
move
where we show
helps to significantly narrow the gap between model and data. This
to
most
all,
and the
clearly stated
time to build on the stylized model and
way
and nearly
theoretical transparency rather than
details. This is the goal of this section,
introducing monetary shocks
in volatility,
be confronted with the data. After
main mechanisms have been
behind them developed,
reality
us that the two industry asymmetries can
in all
countries,
never used.
This
is
the case
we have
studied so
far. In
those countries where k>0, firms borrow
cash from the government and repay the cash plus
completed and output
sold to consumers.
is
Monetary policy consists
distributing the
in
proceeds
random.
10
variance §
in n.
2
a lump-sum fashion
we assume
In particular,
motion on the
in
interval [i,T
],
on cash and then
of setting the interest rate
money and business
the literature on
interest after production is
with
among consumers. As
we assume
cycles,
that the interest rate
changes
is
have zero
that
that
monetary
Let the
initial
distribution of interest rates
be uniform
policy
is
a reflecting Brownian
drift,
instantaneous
and are independent across countries and also independent
,
customary
is
in
[t,T
]
of
changes
and independent
of
the distribution of other country characteristics. Hence, the cross-sectional
distribution of
The
i,
H(i),
does not change over
introduction of
world equilibrium
in
money
time.
leads only to minor changes
in
Equation
(5)
sector do not pay wages, their pricing decision
cash-in-advance constraints affect the firms
(8)
have
to
in
in
addition to labour costs.
be replaced
by:
(16)
pa
=—
-r-e-™
e-1
(17)
pp
=w-e"
10
the description of
section one. Equations (2)-(3) describing the labour-supply
decision and the numeraire rule
face financing costs
in
adequate
still
apply. Since firms
is still
in
given by Equation
the
(6).
final
The
the a- and (3-industries since they
As a
result,
the pricing equations
now
(7)-
11
one takes the view
that monetary policy has objectives other than
the inflation tax is used to finance a public good, shocks to the
marginal value of this public good are translated into shocks to the rate of money growth. Alternatively, if
a country is committed to maintaining a fixed parity, shocks to foreign investors' confidence in the
country are translated into shocks to the nominal interest rate, as the monetary authorities use the latter
to manage the exchange rate.
This simplification
is
if
stabilizing the cycle. For instance,
11
if
We are using the following approximation
here: Ki=ln(1+Ki).
22
Note that changes
the interest rate affect the financing costs of firms and
in
are therefore formally equivalent to supply shocks such as changes
payroll taxes. Formally, this
of earlier
arguments shows
prices are
still
is
that Equations (9)-(1
valid provided
which converges to the
A
the only change required.
we
T
re-define
Y
describing the set of equilibrium
1 )
dFdGdH,
J||(1-5)e
the limiting case
in
B
straightforward extension
(1+A)(7t " n) " Kl
=
p
earlier definition of
production or
in
in
which k-^0
in all
countries.
Financing costs are not a direct cost for the country as a whole but only a
transfer from firms to
consumers
via the
government. Consequently, income and the
\
/
share
of the a-industry are
still
respectively.
Now
more human
capital (high 5)
defined as y =
rich countries
been
simple:
A
for
weaker labour demand
The
and x =
u) e
u.
and S lead
k).
is
is
to a high value of x. This
as
rich.
,
n),
is
why have
However, we have now that
x.
The
intuition is
associated with higher financing costs and therefore a
for all
types of workers.
translated fully into low
size of the a-industry
p -s-e"
—
Remember that,
k leads to both higher income and a lower value for
high value of k
weak demand
•
systems (low
financial
referring to countries with high values for x
a low value
+ pp
s
are those that have better technologies (high
and better
ceteris paribus, a high value for
\p a
is
in
In
the market for skilled workers, this
wages and has no
effects
in
employment.
therefore not affected by cash-in-advance constraints. In
the market for unskilled workers, this
wages and employment. The
weak demand
latter implies
is
a smaller
translated into both lower
(3-industry.
continue to refer to countries with higher values of x as
rich.
Despite
That
is,
it
this,
seems
we
to
shall
us
reasonable to assume that technology and factor proportions are more important
determinants of a country's industrial structure than the degree of financial
development.
We are
ready to determine
how
interest-rate
the cross-section of business cycles. Applying
23
Ito's
shocks affect income growth and
lemma
to the definition of
y,
we
find this expression for the
(demeaned) growth
rate of
income
for the (|n,5,7t,K,i)-
country:
dlny-E[dlny]
(18)
x
=
.®-l + (1-x)-(1 + X)
d(7t-n)+
1+
J
\
+ Xv
dn-(1-x)A-K-di
Equation (18), which generalizes Equation (12), describes the business cycles
as a function
of a (|j,,S,7i,K,i)-country
of
its
industrial structure.
The
first
two terms
describe the reaction of the country to productivity shocks and have been discussed
at length.
shocks.
The
term
third
In particular,
is
new and shows how
shows
it
countries that are poor
is
and have a low degree
decreasing
shocks have larger effects
that interest-rate
3dlny
9di
the country reacts to interest-rate
in
x
of financial
and increasing
in
in
development. That
k (holding constant
is,
x).
d(rc-n)=o
dn=o
An increase
in
the interest rate raises financing costs
industries. This increase is larger in countries with low
development (high
interest-rate
in
Just because of
shocks than
supply of labour
workers
k).
is
rich countries.
inelastic
and the
passed
to
is
degrees
the a- and
(3-
of financial
poor countries are more sensitive to
But there
is
more.
In
the a-industry, the
additional financing costs are fully
the form of lower wages. Production
industry, the supply of labour
partially
this,
in
is
passed
therefore not affected.
In
to
the
f3-
and the additional financing costs are only
elastic
wages. Employment and production therefore decline.
In
the
aggregate, production and income decline after a positive interest-rate shock. But
the asymmetry
stronger
in
in
the labour supply elasticity
poor countries that have larger
is
important, this reaction should be
(3-industries.
reason why poor countries are more sensitive
if
This provides a second
to interest-rate
shocks than
rich
countries.
The
introduction of interest-rate
country-specific shocks
have stronger
shocks provides two additional reasons why
effects
24
in
poor countries: one also works
through their industrial structure and another
financial
a consequence of their lack of
is
development. Both of these considerations reinforce the results of the
To see
previous model.
this,
re-define
dlnY =
f
|
applies since monetary shocks are country-specific
eliminates their effects
in
dFdGdH.
fdlny
and the law
the aggregate. Then, rewrite the
Equation (13)
of large
volatility
still
numbers
and comovement
graphs as follows:
f
V=
(19)
a
x-iLl + (1-x).(1 + A.)
2
(1-T1)
1
+
^
+x
\
1
12
2
+r-K^-(i-xr-A.'
Tl
+ X-v
1+X
C=
(20)
+ X-v
1
a
.
(1-tl)
+
show
that, ceteris paribus,
volatile
which
and
2
•Tl
1
These equations are
^
1+X
'
x .8_1 +(1 _x).(1+X)
2
+ X-v
,,-2
j
natural generalizations of Equations (14)-(15).
countries with low financial development
less correlated with the world.
industrial structure affects the
will
They
be both more
They also show the new channel through
business cycles of countries.
With these additional forces present, the model
closer to the observed cross-country variation
is
in volatility
now
able to
come much
and comovement using
values for 9 and X that are consistent with available microeconomic studies. This
shown
of
in
the bottom panel of Table 2, where
shocks to monetary policy
sample and k=0.5
now
we
in
is
0.1
and
in
we assume
is
that the standard deviation
that k=1 in the poorest countries in our
the richest countries. For 9=2 and X=0.35, the extended model
delivers cross-country differences
estimated
t2
„\2
I*
+r-K^-(1-Xr-X'
Table
1
in volatility
that are nearly identical to the
(-0.024 versus -0.026), and cross-country differences
comovement are now 40 percent
Looking further down the table,
of
those
we can
we observe
further
in reality
improve the
fit
ones
in
(0.165 versus 0.382).
of the
model
in
the
comovement dimension by considering more extreme parameter values. However,
this
is
achieved
at the cost of over-predicting cross-country differences in volatility.
25
We could try to further narrow the gap between theory and
considering additional extensions to the model. But
so
far are sufficient to establish that the
potential to explain at least
countries. This
4.
is
in
part
cycles are different
in rich
and poor
our simple objective here.
From the standpoint
in
think that the results obtained
two hypotheses considered here have the
why business
The Cyclical Behavior
developed
we
data by
of the
of the
Terms
evidence reported
in
of Trade
Table
1
and the theory
the previous sections, the two industry asymmetries studied here are
observationally equivalent. However, using microeconomic estimates for 9 and X as
additional evidence to calibrate the model,
elasticity of
product
we found
demand seems a more promising
cycles are different across countries than the
supply.
section,
In this
that the
we show
that these
asymmetry
explanation of
asymmetry
in
in
the
why business
the elasticity of the labour
two asymmetries have different
implications for the cyclical properties of the terms of trade,
and then confronting
these implications with the data. The evidence on the cyclical behavior of the terms
trade
is
of
consistent with the results of our calibration exercise. Namely, a strong
asymmetry
in
the elasticity of product
demand
helps the model provide a more
accurate description of the terms of trade data than a strong asymmetry
elasticity of
in
the
the labour supply.
We first derive the stochastic process for the terms of trade. Let T((i,5,7t,k,i)
denote the terms of trade of a
(|a,5,7r,K,i)-country.
that the (detrended) growth rate
12
in
Using Equations
the terms of trade
decompose income growth
is
equal
to:
(9)-(1 1),
we
find
12
into the growth rates of production and the terms of trade.
growth rate) measures income growth that is due to changes in
production, holding constant prices. The growth rate of the terms of trade measures income growth that
is due to changes in prices, holding constant production. We follow usual convention and define the
terms of trade of a country as the ideal price index of production relative to the ideal price index of
expenditure. The growth rate of the terms of trade is equal to the share of exports in income times the
growth rate of their price minus the share of imports in income times the growth rate of their price.
It
is
possible to
The growth
rate of production (or
GDP
26
dlnT-E[dlnT] = --d(7i-n)+
(21)
v
(X
9
1
^
-dn
+ A-V
Equation (21) describes the cyclical behavior of the terms of trade as a
function of the country's industrial structure.
shocks
to productivity affect negatively the
It
shows
that positive country-specific
terms of trade, and
adlnT
absolute value) the richer
the country,
is
is
i.e.
this effect is larger (in
negative and
ad(Tt-n) dn=o
decreasing
in x.
Equation (21) also shows that positive global shocks to productivity
worsen the terms
~\f-i
I—
of trade of
poor countries and improve those of
rich countries, i.e.
T
is
adn
negative
if
x<v and positive
if
x>v. Finally, Equation (21
)
shows
that
d(n-n)=0
interest-rate
shocks have no effects on the terms
behind these results
of trade.
We discuss the intuition
in turn.
Country-specific shocks to productivity have no effect on import prices
because countries are
small. But they
do
affect export prices.
Consider a positive
country-specific shock to productivity. In the a-industry, firms react to the shock by
producing more of each variety they know
increase
in
the production of each variety
how
is
to produce. Since this set
large.
varieties are imperfect substitutes, the increase
country's a-products. In the P-industry, firms
react to the
(or
shock by spreading
by forcing
some
do
this).
production lowers the price of the
to
among a
As a
small, the
Since domestic and foreign
know how
their production
firms abroad to
in
is
result,
produce
large
all
varieties.
number
the increase
in
They
of varieties
the
production of each variety
is
infinitesimally small
products are not affected.
In
the aggregate, the terms of trade worsen as a result of
the shock. But
terms
of trade
if
the
asymmetry
in
the elasticity of product
should deteriorate more
Global shocks influence
all
and the prices
in rich
of the country's p-
demand
is
important, the
countries.
countries equally and, consequently, they do not
affect the prices of different varieties of a-
and P-products
27
relative to their
corresponding industry aggregates. Consider a positive global shock to productivity.
We saw earlier that this shock
lowers the price of
products (See Equation (11)). The reason
in
productivity leads to a direct increase
elasticity of
the labour supply
employment
(3-products.
of unskilled
is
in
is
all
simple:
(3-products relative to
both industries, the increase
In
production. But
important, the increase
workers and leads
As the world supply
a-
all
in
the asymmetry
if
in
the
productivity raises
to a further increase in the production of
of (3-products increases relative to that of a-products,
their relative price declines. This
is
why
the terms of trade of net exporters of
|3-
products, x<v, deteriorate, while the terms of trade of net importers of p-products,
x>v, improve.
Finally,
effects
country
Equation (21) states that country-specific interest-rate shocks have no
on the terms
is
small. But they
interst-rate
shocks do not
affect the prices of
These shocks do
of trade.
do not
affect export prices either.
relative to the industry
shocks
affect the production of (3-products.
change
their prices in the
makes
cyclical behavior of the
affect the
terms
comovement graphs
result,
they do not
aggregate. Interest-rate
in
the p-industry cannot
do not
how
affect the
terms
of trade.
the two industry asymmetries shape the
of trade. In the
absence
of
asymmetries
in
the elasticity
only country-specific shocks affect the terms of trade.
the absence of asymmetries
shocks
clear
terms
A—>0,
of the labour supply,
As a
earlier,
face of perfect competition from firms abroad. Therefore,
country-specific monetary shocks
)
However, firms
because the
As discussed
affect the production of a-products.
domestic varieties
Equation (21
not affect import prices
in
the elasticity of product
of trade.
for the
demand,
This has implications for the
terms
of trade. Let
8-^°=, only global
volatility
VT (fi,5,Tr,K,i) denote
and
the standard
deviation of the (detrended) growth of terms of trade of a (|a,8,7t,K,i)-country,
C J (\i,5,n)
denote
(13), (21)
and the properties
its
correlation with world
In
and
let
average income growth. Using Equations
of the shocks,
we
28
find that:
V T =a-.
(22)
(x-v)-A
+
(1-il)
Tl
CT
(23)
=
"l
V?
+ X-v
+
'ix-v)X^
•Tl
fl-<1-1>
To understand the
extreme cases. Both are
comovement graphs
values.
is
Assume
first
the asymmetry
VT = — a
in
1
+ X-v
behind these formulae,
intuition
illustrated in Figure 4,
terms
of the
that the only
of trade
and C T =
prices
is
.
is
it
demand,
volatility
graph
i.e.
differ
and
parameter
across countries
A=0. Then,
upward
is
volatility
x, for different
reason why business cycles
The
useful to consider two
which plots the
as functions of
the elasticity of product
•y/l-'n
•
+ A.v
1
V
sloping. Since
all
the
G
volatility in
of trade are
more
due
changes
to
in
the domestic varieties of a-products, the terms
volatile in rich countries
The comovement graph
of the a-industry is large.
zero. While the terms of trade
is flat at
country-specific shocks, world
where the share
income responds only
respond only
to
shocks. As a result
to global
both variables are uncorrelated.
Assume
countries
VT
is
the
lx-v|-X
=
J
!
1
next that the only reason
asymmetry
i—
cr-AH an d
in
+ A.v
1-1
[
all
if
x < v
if
x >v
.
i
1
the
volatility in
aggregate industry prices, the terms
share
cycles are different across
the elasticity of the labour supply,
T
C =
a minimum when x=v. Since
why business
The
of trade are
more
of interindustry trade in overall trade is large,
very rich and very poor countries
whose
is
due
i.e.
is
to
changes
Then,
like
in
|
x-v
|
is
large.
a V, with
the
volatile in countries
factor proportions
most from world averages. The comovement graph
0^><».
graph looks
volatility
prices
i.e.
where the
These are the
and technology
differ
the
a step function with a single
step at x=v. Since global shocks drive both the world cycle and the terms of trade,
these variables are perfectly correlated.
If
the country
29
is
a net exporter of a-products,
this correlation is positive.
correlation
The
is
If
the country
a net exporter of (3-products,
is
negative.
volatility
and comovement graphs
for the
combination of these two extreme cases, as shown
looks
like
while the
v.
a
V
that has. been shifted to the right of
comovement graph slopes upwards
The extreme cases are
terms of trade are
in
Figure
4.
The
source of differences
with
flat tails
elasticity of the
is
business cycles. The more important
comovement
graph.
the slope of the
comovement
is
is
graph
because they
is
asymmetries as a
the
volatility
The more important
labour supply, the closer
volatility
and a steep slope around
useful not only to build intuition, but also
product demand, the higher the slope of the
the slope of the
higher
in
general a
in
x=v and rotated counter-clockwise,
point to a criterion to determine the relative importance of the two
elasticity of
this
asymmetry
in
graph and the
the asymmetry
the volatility graph to a V-shape
in
the
flatter
the
and the
graph.
Before going to the data however, note that there
is
an alternative
interpretation of these patterns within our theory. Independently of the values for
and
A.,
the larger
the slope of the
r|=0,
is
the country-specific
volatility
graph and the
V T = — a and C T =
component
flatter
Also, the
.
productivity shocks, the closer
is
the
the slope of the
more important
volatility
graph
,
the slope of the
of productivity
for the
terms
country-specific
of the
of trade
of
-,-
T
a and C =
+ A. v
•
volatility
as providing evidence on the
and global components
If
of
is
[-1
if
X < V
[1
if
x >v
and comovement
relative
importance of the
shocks, instead of the relative importance
two industry asymmetries.
Figure 5 plots the empirical analogs of the terms of trade
comovement graphs.
in
component
a V-shape and the higher
!
Therefore, one could also interpret the shape of the
comovement graph.
the global
Ix-vl-X
comovement graph .|fn=1,V T =J
1
graphs
to
is
shocks, the higher
Figure
1
In
volatility
and
contrast with the very clear unconditional patterns apparent
for the volatility
and comovement
30
of
income growth,
in
Figure 5
we see
and comovement
that the volatility
significantly correlated with
of fluctuations in the
income. However,
the
the introduction, there
in
of trade
and comovement
a significant positive
partial correlation
comovement and income remains
the third column of Table 3
the asymmetry
in
function, respectively).
median
we
is
We do this by interacting
income.
from zero.
dummy
this,
we
and a step
sample
no evidence
find
in
two
at the
of the non-linearity
when we
the sample at different points (not reported for brevity).
In light of
graph and a
flat
as evidence
in
the discussion above, this pattern of an upward sloping
comovement graph
for the
terms
of trade could
favour of the relative importance of asymmetries
product demand, or as evidence
in
volatility
be interpreted either
in
the elasticity of
favour of the unimportance of global shocks.
However, there are good reasons to prefer the former interpretation over the
Consider
for
example the
calibrations
comovement
of
correlation
productivity shocks, Jr\
in
income growth,
that cross-country correlations
story,
Table
2. In
was necessary
it
in
in
,
and so the evidence on terms
to
assume
ranged from 0.25
productivity
product
demand over
Finally
we observe
country differences
in
the
that the
volatility
in
the terms of trade of the
same
to 0.40. This
suggests to us
of the
and comovement should be
asymmetry
in
the elasticity of
the elasticity of the labour supply.
model
is
able to replicate the observed cross-
and comovement
reasonable parameter values. The
that the cross-country
shocks are an important part
of trade volatility
the asymmetry
latter.
order to replicate the observed
interpreted as favouring the relative importance of the
for
when
both the intercept and the
variable that divides the
When we do
In
and
important, the volatility
non-linear functions of income (V-shaped
on income with a
level of
insignificantly different
predicted by this version of the theory. Moreover, our results do not change
split
we
between
take seriously the prediction of the theory that
the labour supply elasticity
comovement graphs are
coefficient
the second column of Table 3
the terms of trade and income, while the partial correlation between
volatility of
terms
is
of trade are not
of volatility
sources
find that, controlling for other potential
discussed
in
terms
right
of the
terms
of trade fairly well
panel of Table 2 reports the results for
calibration exercised discussed previously
31
in
the
context of the
volatility
and comovement
of
income growth. For a value
find that the theory predicts cross-country differences in
when
0.012 and 0.010
respectively. This
the elasticity of unskilled labour supply
compares favourably
the regression with controls
in
no cross-country differences
X=0, but
it
somewhat
terms
Table
in
we
of 9=2,
of trade volatility of
is
A.=0 or
X=0.35
with the predicted difference of 0.009 from
Regarding comovement, the theory predicts
3.
terms of trade comovement whatsoever whenever
overpredicts cross-country differences
in
comovement when
in
both physical and
X=0.35.
5.
Trade Integration
The postwar period has seen a
policy barriers to international trade
paper
is
in
substantial reduction
goods.
Remember that
As
transport costs decline, the prices of products
country has comparative advantage increase and the share
As a
industries increases.
argument
result, industrial structures diverge.
one should expect
that
is
we add
transport costs to the
We generalize the model
transport costs t>1
at the destination
.
If
implies that domestic
model and confirm
by assuming that trade
x units of output are
and the
and
shipped from
rest "melt" in transit.
We
re-define P a
pa
(z)
and p p
D
(z)
be the
c.i.f.
and P p as the
production of these
A
natural conclusion of
In this
this intuition.
is
subject to "iceberg"
origin, only
in
one
unit arrives
of transport costs
ideal price indices of the a-
and keep the numeraire
The domestic
32
and
the a- and (^-industries,
or domestic price of variety z
the (|i,5,n;,K,i)-country, respectively.
its
which a
international product prices might differ. Define p o (z)
industries using international prices,
D
in
business cycles.
in
The presence
p p (z) as the f.o.b. or international price of variety z
respectively.
of this
that reductions in transport costs
(globalization?) should increase cross-country differences
section,
in
theme
depends on
that the nature of business cycles that a country experiences
industrial structure.
this
the main
in
rule in
and
(3-
Equation
(5).
Let
the a- and (3-industries
price of imported varieties
is
in
D
p a (z)=xp a (z) and p p (z)=rp p (z), while that of exported varieties
D
p p (z)=p p (z).
If
some
there are
D
follows: p a (z)<p a (z)<x-p a (z)
case
varieties that are not traded, their price
D
and p p (z)<p (z)<xp
E,
converge and the model
international prices
one here. As t-»1 and k->0
of the
p a (z)=p a (z) and
is
As
(z).
t-»1, domestic
bounded as
and
fJ
of section three obtains
in all
is
model
countries, the
as a special
of section
one
obtains.
The
introduction of transport costs leads to
The maximization problem
of the world equilibrium.
and Equations
some changes
of the
goods sector
of the firms in the final
D
(24)
consumer
(2)-(3) describing the labour-supply decision
relevant prices for firms are the domestic ones. First,
p F =(Pa
v
-(P
)
D
in
Equation
(6)
are
we must
not affected
valid.
now
But
the
replace the pricing rule
)
D
ideal price indices of the a-
Given the cost function
produce the domestic varieties
all
is
by the following one:
and
(3-industries using
domestic prices. Consider next the pricing decisions of firms
almost
still
the description
D 1v
p
where Pa and P 3 are the
industries.
in
of their production
in (4)
and the
the a- and
in
fact that foreign firms
of a-products, firms in the a-industry
and the domestic
price
is
(3-
cannot
always export
the international one,
i.e.
D
p a (z)=p a (z). Therefore, Equation (7) describing the pricing behavior of domestic
producers
of
a-products
still
applies.
We must however replace
Equation
(8)
by the
following:
(25)
pf=w-e-"
To complete
equilibrium prices.
that Equation (9)
in
A
the description of the model,
we need
to
compute the
straightforward extension of the arguments
is still
valid
as description
in
set of
section two
shows
of the relative prices of different varieties
the a-industry. However, finding the prices of (3-products
33
in different
countries and
l
the international relative price of the a- and p-products
appendix provides a detailed derivation
intuition
behind them and
In equilibrium,
is
quite involved.
these prices. Here
of
we
simply discuss the
their implications.
poor countries export P-products to
rich countries. In
income countries, P-products are not traded. The appendix shows
classify countries into these three
groups as
0i,5,7T,K,i)eM
yP
iff
U/
1
^
^
9
iff
1
x"
-^-'"-n) -^-'
c- t
-(1-5)
v
'
.
a
Te
<
e
e-1
^
v
'
9
5
e ~i^7
K i)eX
^v< Y
T
iff
I
p
2=1
where ¥a
x
is
defined as before and W.
generalizes the previous one.
is
time-invariant
in
An
is
"n)
(,I
lT^ K < T ^»
-(1-5)
8-1
1
I
c1
c
Av
t-"
(jx,5,7t
we can
e-i
-8 e
9
1
(h,8,71,k,i)eN
that
middle-
follows:
2
(26)
The
^
t"
9
Xv
'
S9
-^7-'"- n)
c
l^- K "
-(1-5)
a new constant that depends on x and
important characteristic of this classification
an important sense: the
fraction of countries of
is
that
each type that
belongs to each group does not vary with the world cycle.
The appendix shows
that
international relative prices, but
we can
we must
still
use Equation
(1 1
)
as a description
of
replace Equation (10) by the following one:
34
it
if
(|a,5,Tl,K,l)G
X
if
(u,5,7t,K,i)e
N
if
(|^,5,7i;,k,i)g
M
1
9-1
1
^•^•5
Pp
1+A-v
e
-(n-n)
IE!
^« 9
-x"
Xv
ki
1+Xv
1+Xv
(27)
(1-5)
Unlike the previous models, purchasing power parity no longer applies.
see
this,
note that the price of the
final
good
is
now
To
given by:
1-v
(28)
pF
=x
v
'PP
y
V
J
To understand
an
this equation,
remember
infinitesimal part of the total expenditure
ideal
basket of a-products
the numaraire rule
in
countries purchasing
is
x-P a
Equation
power
.
The
in
that
domestic oc-products constitute
a-products, so that the price of the
price of (3-products
however
pp
.
Finally,
use
Since the prices of (3-products vary across
(5).
no longer applies and the cost
parity
D
is
of living
is
higher
in
countries that import (3-products. Consistent with existing evidence on the cost of
living,
the theory predicts these countries to be the rich ones.
13
We are ready to characterize the cross-section of business cycles in this
extended model.
Now income and
the share of a-products are
d
prices.
That
find that the
/
is,
y = (p„
•
s + p°
\
•
u)-
(demeaned) growth
e
n
and x =
rate of
d
—
income
measured
-s- e"
.
is still
Applying
Ito's
in
domestic
lemma
to y,
we
given by Equation (18).
Consequently, Equations (19) and (20) relating the properties of business cycles to a
country's industrial structure
The assumption
to the
same
that the final
transport cost
still
good
is
hold.
And Equations
nontraded
is still
x.
35
(22)-(23) describing the cyclical
not binding, provided that the latter
is
subject
properties of the terms of trade also apply. So, what are the effects of transport costs
on the cross-section
and, as a
result,
of
business cycles? Transport costs reduce the volume of trade
the cross-sectional dispersion
in x.
To see
this,
we compute
the
cross-section of shares:
e-1
1
Yp-n
e
-5
e
_
tl
1-v
(29)
V]i°-5
v
1-v
The
x
-x-
is
if
(|j.,8,7i,K,i)e
N
-(X+9
_1
if
(^,5,7l,K,l)€
M
)(7t-n)-AKi
°=1
Ta
e
t-
,
Xv
-(1-8)
high enough, trade
the greater are the differences
mean
in
(3-products disappears
becomes
in industrial
14
flat.
i.e.
the a-products
and x=v
The lower
in rich
in
production remains constant. But changes
in rich
Lower transport
countries and the [3-products
in relative
employment and production. The lower are transport
production of (3-products
countries.
which a country has
poor ones. Higher relative prices imply higher industry shares
if
in all
the transport costs,
structures of countries.
higher relative prices of those products
comparative advantage,
even
l)eX
((li8|
(1-6)
8
cross-section of business cycles
costs
^
jf
1-V
1-x
If
HV
,
AV
- ( x + 9-).(.-n)-x.K,
e
for
those products,
prices also affect
costs, the lower
countries and the higher
is in
in
is
poor ones.
these two channels, increased trade integration magnifies differences
in
the
15
Through
the industrial
structures of countries.
An
interesting result that follows from this discussion
affects differently the business cycles of rich
If
the elasticity of substitution
would
there
still
is
vary and there would
no trade
in
is
that trade integration
and poor countries.
In rich
countries,
between a- and (3-products were different than one, industrial structures
still be some differences in business cycles across countries even
if
^-products.
15
These increases in employment could come from increased participation or reduced unemployment,
as is the case in the model presented here. Or they could come from employment in other industries, as
it would be the case if we changed our assumptions and allowed both industries to use both types of
workers.
36
trade integration increases the share of a-industries and
to country-specific shocks. This leads to
more synchronized
makes them
business cycles that are less
less sensitive
volatile
and
with the world cycle. In poor countries, trade integration increases
makes them more
the share of (3-products and
This leads to business cycles that are
more
sensitive to country-specific shocks.
volatile
and
less synchronized with the
world.
The welfare consequences
to assess.
the
As
absence
of trade integration for
usual, there are the standard welfare effects that would occur
it
also might
change the
among
products and therefore re-distribute income
that there are also welfare effects that
business cycles.
accumulation.
As a
consumers are
integration as
6.
Remember
risk
result,
in rich
volatility
relative price of a-
is
even
and
[3-
come from changes
trade
equal to consumption.
To
in
in
the nature of
assets and capital
the extent that
countries welfare improves as a result of trade
declines.
The opposite
is
true
in
poor countries.
16
Concluding Remarks
This paper started with the observation that business cycles are different
rich
in
countries. But the theory here
we have assumed away
income
averse,
income
that
difficult
Trade integration increases efficiency and
of fluctuations in productivity.
raise welfare everywhere. But
shows
a given country are
and poor countries.
In particular
fluctuations in per capita growth are less volatile
and more synchronized with the world cycle
in rich
countries than
in
poor ones.
explored the possibility that these patterns might be due to differences
structure.
Comparative advantage leads
use new technologies operated by
face inelastic product
rich
skilled
demands and
in
countries to specialize
workers.
in
We
in industrial
industries that
We argued that these industries
labour supplies. Under these conditions the
16
If there were some trade in assets, it is not clear whether the welfare effects of trade integration would
be always positive in rich countries and negative in poor ones. On the one hand, volatility increases in
poor countries and this lowers the value of their assets. On the other hand, comovement with the world
declines in poor countries and this increases the value of their assets.
37
income
effects of country-specific supply
generate reductions
in
prices
shocks tend
and only small increases
advantage also leads poor countries
demands and
use
traditional
We argued that these industries face
shocks tend
to
be
large, since they
generate
little
on prices and large effects on employment.
Our
model
employment. Comparative
labour supplies. Under these conditions, the income
effects of country-specific supply
effects
in
be moderate, since they
to specialize in industries that
technologies operated by unskilled workers.
elastic product
to
to
been
contribution has
study their implications.
to
A
frame these hypotheses and provide a formal
simple calibration using available microeconomic
estimates of the key parameters suggests that these hypotheses have the potential
to
account
for
observed cross-country differences
that cross-industry differences
in
product-demand
important than cross-industry differences
for
observed cross-country differences
quite flexible
and allows us
examined how differences
to
in
in
in
business cycles. Also,
elasticities
are quantitatively more
labour-supply elasticities
in
we find
in
accounting
business cycles. The model turns out to be
analyze a number of related issues. For instance,
financial
development
affect the
way
we
countries react to
shocks, the implications of the theory for the cyclical behavior of the terms of trade,
and the
effects of globalization
on the nature
The next step however should be
of
business cycles.
empirical.
The theory developed here
provides a rich set of testable hypotheses relating the industrial structure of countries
with the properties of their business cycles.
preliminary.
These hypotheses are promising,
They should be thoroughly confronted
38
with the data.
but
still
.
References
Acemoglu, D. and F. Zilibotti (1997) "Was Prometheus Unbound by Chance?
Diversification and Growth," Journal of Political Economy 1 05: 709-751
Risk,
Backus, D.K., P.J. Kehoe and F.E. Kydland (1995), "International Business Cycles:
Theory and Evidence" in T.F.Cooley (ed.) Frontiers of Business Cycle Research,
Princeton University Press.
Baxter, M. (1995), "International Trade and Business Cycles" in G.M. Grossman and
Handbook of International Economics, Volume 3, North-Holland.
K. Rogoff (eds.)
Banks, A. (1979), Cross-National Time-Series Data Archive, Center for Social
Analysis, State University of New York, Binghamton.
Eichenbaum and C. Evans (1997), "Sticky Price and Limited
Models of Money: A Comparison," mimeo.
Christiano, L, M.
Participation
Davis, D. (1995), "Intraindustry Trade: A Heckscher-Ohlin-Ricardo Approach,"
Journal of International Economics 39: 201 -226
"New Product Varieties and the Measurement
American Economic Review 84: 157-77.
Feenstra, R. (1994),
Prices,"
of International
J. and D. Romer (1999). "Does Trade Cause Growth?". American
Economic Review. 89(3):379-399.
Frankel,
Harrison, J.M. (1990), Brownian Motion and Stochastic Flow Systems, Krieger.
C, K.M. Murphy and R.H. Topel (1991), "Why Has the Natural Rate of
Unemployment Increase Over Time?" Brookings Papers on Economic Activity,
Juhn,
Vol.2,
pp.75-143.
Kydland, F.E. and E.C. Prescott (1992),"Time to Build and Aggregate Fluctuations,"
Econometrica, 50: 1345-1370.
and H. Lai (1999). "The Gains from Trade: Standard Errors With the
Monopolistic Competition Model". Manuscript, University of Toronto.
Trefler, D.
39
CES
Appendix
1
Data Description
:
Our sample consists
of
76 countries
which
for
we have complete
annual data
over the period 1960-1997 required to construct income growth and terms of trade
We
growth.
measure per capita income growth as the sum
growth plus growth
of real
the terms of trade. Data on real per capita
in
per capita
GDP
GDP
growth are
drawn from the Penn World Tables and are extended through 1997 using per capita
GDP
growth
constant local currency units from the World Bank World
in
Development
We construct growth
Indicators.
the terms of trade as the growth
in
in
the local currency national accounts deflator for exports multiplied by the share of
GDP
in
current prices adjusted for differences
less the growth
in
the local currency national account deflator for imports multiplied
exports
in
by the share of imports
purchasing power
in
parity.
GDP
in
in
purchasing power
current prices adjusting for differences
trade
volatility
in
Data on import and export deflators and current price trade
shares are from the World Bank World Development Indicators, and
factors are from the
parity,
Penn World Tables.
Prior to
PPP
conversion
computing income and terms
of
and comovement, we discard 33 country-year observations
constituting about
1
percent of the sample where measured growth
in
the terms of
trade exceeds 20 percent. Each of these cases occurs during episodes of very high
where growth
inflation
in
very noisy signal of true
The
oil
movements
is
a
dummy variable
all
other countries
This variable
is
in
one
the World
if
the country
the World
variable
Bank World Development
we
of
classified
a weighted average of countries' distances
Romer
to their bilateral trade.
(1999). Data on revolutions
coups are taken from the Banks (1979) dataset. The standard deviation
computed as the standard deviation
is
Bank World Development
where the weights are proportional
taken from Frankel and
extreme and provides a
from the following sources. Primary
taking the value
is
is
import and export prices.
exporter or a commodity exporter
Indicators. Trade-weighted distance
from
in
control variables are obtained
product exporter
as an
the import and export deflators
growth rates of the
Indicators.
GDP
and
of inflation is
deflator taken from
To avoid extreme
outliers in this
discard 204 country-year observations constituting seven percent of the
40
sample where
inflation
exceeds 100 percent per year
computing the standard
prior to
deviation of inflation.
The data are
Appendix
2:
section
in
five.
*F
p
we compute
the world equilibrium
=JJJ P
P
p
,
V
model
x~
Xv
(1
- 8) e (1+X) {n
~ n) - K
p p =Pp, Tpis constant over time. This
D
If
p p =P p and k—>0
in all
corresponding constant of the real model
general model of section
for *F
l
•
•
dF dG dH
•
•
J,
of section four.
problem
the model with transport
Define the following object:
D
If
in
nV +Xv
f
(A1)
upon request.
Equilibrium Prices with Transport Costs
appendix,
In this
costs
available from the authors
in
is
the case studied
countries,
¥.
section two.
in
the monetary
simplifies to the
We show next that in the
the world equilibrium can be computed as a fixed-point
five,
.
p
First,
we
derive a relationship that ensures that international prices clear world
markets, for a given set of domestic prices. Equating the
the a- and (3-industries,
ratio of
world spending
in
v
,
to the ratio of the value of their productions,
1-v
fffp a
I
se'
dFdGdH
we
find that Equation (11) is
still
valid,
provided
we use
the
JjJpp-u-e'-dF-dG-dH
1+X-v
definition of
Y
p
write Equation
in
Equation (A1). Define Z
(1 1)
as follows:
41
e
An
.
Then,
we can
re-
(A2)
Yo=Ta
-Z
(
where
*F„
e
H
— —
e
e-1
1
-5
e
e-1,
9
N
_.
(n-ri)
dFdG
e
as
,
in
the text. This equations defines
J
v
a linear relationship between Tp and Z that has a simple economic interpretation:
—
Pb
Taking as given the set of domestic prices (remember that the distribution of
is
PP
implicit in
T
p
),
P
—
P
Equation (A1) describes the international prices (remember that
P
implicit in Z) that equilibrate
Second,
we
world markets.
derive a relationship that ensures that domestic prices clear
domestic markets, for given international prices. To do
in
assume
first
P-products are nontraded goods. Then, equating the
(|a,S,7i,K,i)-country
spending
this,
the a- and (3-industries,
v
,
to the ratio of the
income
that in the
ratio of
of both
1-v
D
industries,
1
p -s-e'
^
p°-u-e*
,
we
find that:
110-1
(A3)
^=
Z-
"
.9
-(1-5)
V,
Xv»V
"
This domestic price of p-products holds
exceeds the price
at
which domestic
does not exceed the price
at
(3-firms
which firms
in
in
can
the
equilibrium
sell
if
and only
if:
(i) it
P-products abroad; and
(ii) it
goods sector can purchase
final
P-
products abroad. These conditions define three sets of countries: X(Z), N(Z), M(Z).
1
We say that (n,8,7t,K,i)e M(Z)
if
and only
if
z
•
——
Xv
t"
42
9-1
1
IT/
fl
C
A+O
fi
-(1-8)
e
1+Xv
A
1+Xv *'
<
1
.
We
is
.
1
also say that
N(Z)
(u.,5,:n:,K,i)e
if
and only
if
<z
1
e-1
1
.„e .5
xj/e
1 a
T"
_A±^. (Tt _ n )-^. K1
e
ItAv
Xv
1
8-1
X+8~'
Finally, (n,8,7i,K,i)eX(Z)
and only
if
T
if
^<z- ^1
t-'
the
membership
of
membership
of the different
the
membership
of
with
Z.
M(Z)
i+av
non-increasing
is
G(n-n) and
groups varies only with
The membership
Z depending on
With
e
_
Kl
i+xv
.
,.
Define
-(1-5)
distribution functions F((j.,5,k),
the
in
-
a group as the fraction of countries of each type that belongs to
each group. Since the
decreasing
X
,
,
(7l-n)
5
tA "
v
< X 1+Xv
-(1-5)
1
'
1+Xv
in
H(i) are constant,
Z. In particular,
Z and the membership
of N(Z) could increase,
we have
of X(Z) is
that
non-
decrease or stay constant
the distribution of country characteristics.
we can
hand,
this notation at
write the relative prices of (3-products that
as a function of Z as follows:
_1+Xv
vpe
'9
T
2
(A4)
.5
u
u e9 .X
11
.
.
*+8
6
M-
ct
-X-v
M(Z)
if
(|i,5,7i,K,i)e
if
(n,5,7t,K,l)6N(Z)
if
(n J 8,7i,K,i)eM(Z)
6-1
2
1
1+i-v
,
c
*
„,
n-n)
ki
1+Xv
1+Xv
(1-§)
Equation (A4) also has a simple economic interpretation: Taking as given
international prices, this equation describes the set of
domestic markets. Substituting Equation (A4)
Y
p
=
- 8) e {UX)in
' n) - K '
•
JJJ(1
•
into
Equation (A1)
dF dG dH +
•
•
X(Z)
e-1
1
1
(A5)
+wyZ^[L
Q
-6
v
e-1
v
dFdG +
e~
N(Z)
+t
•
JJJ(1
- 6) e (1+x >("-n)-K
-i
dF dG dH
.
.
M(Z)
43
domestic prices that equilibrate
we
find:
.
Equation (A5) defines a function Yp = Tp(Z) that
*
Y
decreasing and bounded: lim
lim
^=
x
-
•
constant
T
y
=
f f|(i
p
x|
•
e
(1+X) (n- n) - Kl
is
+
•
continuous and non-
e WH»*)-™ dF
•
•
•
dG dH
•
and
>
-
obtained by crossing (A2) and (A5). That
is,
the
refer to in the text is implicitly defined by:
- 5) e
<
1+A H«-n)-K
•
.
dF dG dH +
.
.
Ie
VV
"
19
jjl
V
X
e
!
!
(A6)
5)
dF dG dH <
•
equilibrium
we
that
JjJ(1
'
5)
JJJ(1
The world
-
=
p
is
'
-
59
"
-l (n -n)
e6
dFdG +
N|^
+T
'
JlfC
_8
>
•
e
(1+M(It - nhKl
•
dF dG dH
•
•
M
It
is
unique.
In
degree
of
straightforward to
the text,
show
we assume
smoothness
that
this is
an equilibrium
the case. This
is
exists.
But
it
equivalent to imposing enough
to the distribution functions F(|li,8,k), G{n-Yl)
44
might not be
and
H(i).
.
—
CO
t
o
LJJ
c
o
T3
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:=
EiS c o
TO O 3
CO >
o
cz
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_
CQ
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=5
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g
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TTi
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—
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CD
oi f;
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c >
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r-
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£
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<-
fc
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Table
2:
Calibrations
Cross-Country Differences
in Volatility
and Comovement
Terms
Volatility
ComovemRnt
Volatility
Growth
Comovement
-0.026
0.382
0.009
0.037
Income Growth
of Trade
Empirical
Point Estimate
Theoretical, Basic
e
Model
X
CO
cxt
oo
0.35
0.7
2
2
2
0.35
0.7
1.2
1.2
1.2
0.35
0.7
a
Vn
0.04
0.40
0.000
0.000
0.000
0.000
0.03
0.38
-0.005
0.047
0.001
2.000
0.37
-0.009
0.078
0.002
2.000
0.05
0.31
-0.011
0.098
0.012
0.000
0.04
0.30
-0.016
0.129
0.010
0.343
0.04
0.31
-0.019
0.149
0.009
0.623
0.06
0.25
-0.025
0.186
0.026
0.000
0.05
0.25
-0.027
0.200
0.020
0.171
0.04
0.26
-0.028
0.208
0.016
0.330
0.03
Theoretical, Monetary Model with K (x)= =i.i-x,4> =0.1
e
CO
0.04
0.40
0.000
0.000
0.000
0.000
=o
0.35
0.03
0.38
-0.015
0.108
0.001
2.000
oo
0.7
0.03
0.37
-0.038
0.189
0.002
2.000
0.05
0.31
-0.011
0.098
0.012
0.000
2
2
0.35
0.04
0.30
-0.024
0.165
0.010
0.343
2
0.7
0.04
0.31
-0.045
0.219
0.009
0.623
0.06
0.25
-0.025
0.186
0.026
0.000
1.2
1.2
0.35
0.05
0.25
-0.034
0.219
0.020
0.171
1.2
0.7
0.04
0.26
-0.052
0.249
0.016
0.330
This table compares empirical differences in volatility and comovement of real income growth (left panel) and
terms of trade growth (right panel) with the predictions of the basic model of Section 2 (top panel) and the model
with monetary shocks of Section 4 (bottom panel). The first row reports the estimated difference in volatility and
comovement between the richest countries in the sample (with log per capita GDP = 9.5) poorest countries in the
sample (with log per capita GDP = 6.5), based on the regressions with controls in Tables 1 and 3. The remaining
rows report the predictions of the model for the difference in volatility and comovement between a rich country
(with x=0.6) and a poor country (with x=0. 1 ), for the indicated parameter values.
Table
Volatility
3:
and Comovement
of
Terms
of Trade
Growth
Volatility
Basic
With Controls
With Controls, Nonlinearities
Coef
Std.Err
Coef
Std.Err
Coef
Std.Err
0.023
0.013
-0.034
0.013
-0.048
0.030
0.000
0.002
0.003
0.001
0.005
0.004
Primary Product Exporter
0.004
0.003
0.005
0.003
Trade-Weighted Distance
0.006
0.002
0.006
0.002
-0.007
0.010
-0.008
0.010
0.145
0.020
0.138
0.025
Intercept
ln(Per Capita
GDP
Revolutions and
at
PPP)
Coups
Std.Dev. Inflation
Dummy for
Rich Countries
0.036
0.043
Dummy for
Rich Countries x
-0.004
0.006
ln(Per Capita
GDP
at
PPP)
R-Squared
Number
of
Observations
0.002
0.565
0.570
76
76
76
Comovement
0.004
0.159
-0.026
0.252
0.062
0.419
0.014
0.020
0.012
0.028
-0.001
0.060
Primary Product Exporter
-0.001
0.063
0.012
0.064
Trade-Weighted Distance
0.018
0.028
0.021
0.028
0.032
0.221
0.058
0.238
-0.089
0.427
-0.318
0.478
Intercept
ln(Per Capita
GDP
Revolutions and
Std.Dev.
at
PPP)
Coups
Inflation
Dummy for
Rich Countries
0.644
0.775
Dummy for
Rich Countries x
-0.068
0.096
ln(Per Capita
GDP
at
PPP)
R-Squared
Number
of
Observations
0.005
0.012
0.036
76
76
76
This table reports the results of cross-sectional regressions of the standard deviation of terms of trade growth
(top panel) and the correlation of terms of trade growth with world average income growth excluding the country
in question (bottom panel) on the indicated variables, for different samples and control variables. Poor (rich)
countries refer to countries below (above) median per capita GDP. In the columns labelled 1960-79 and 198097 volatility and comovement are calculated over the indicated subperiods. The control variables consist of a
dummy variable which takes the value one if the country is an oil or commodity exporter, a measure of tradeweighted distance from trading partners, the average over the period of the number of revolutions or coups, the
standard deviation of inflation, a dummy for countries with income greater than the median, and an interaction of
this dummy with per capita GDP. See Appendix for data definitions and sources. Standard errors are
heteroskedasticity-consistent. *** (**) (*) indicate significance at the 1 (5) (10) percent level.
47
Figure
1
and Comovement
Volatility
:
Volatility
0.14
-
y = -0.0133X + 0.1612
n rwa
£- 0.12
R2 =
-
D
D NGA
S
o
D
3
o.i
TCO
D COG
-
D
CD
D
E
§ 0.08
yl^TSTGO Q
-
D BGD
LSO
^D
Da
MR!
S
-
0.04
-
D MW
'
D
D
„
CAFc
>
DZA
D
EMDPER
FN
D
D
«
ITO
LUX
pry
DN
ISL
D MYS
PR
P
p WG
ISR
a9 iKG
j^"^^
THA
'
f
ESP
CD
2
D
f
^^P*--
GHA
CD
ft.
ft
emj^^a
0.06
GAB
D MUS
NER
'
§
o
0.2941
GUY
aTJWw-.,
D GT0 ca
0.02
-
-
7
6.5
(5
7.5
8
9
8.5
9.5
10
ln(Per Capita Income)
Comovement
0.8
-
0.6
-
CAN
NLD
c £
!Io
o
<d
£
0.4
-
arcg
E £
11
Dia
DTGO
a
0.2
-
„
«5o
nmo
DGIM
D Ca
D BEN
DaC1S
dzmb
D,HA
caf
ZAR
pD-SHfi
_^——
D
n
-
nc*
QEEfc
D ^ 6b
-""
PRY
tJSlMNGA
CHN
rtrP
,
„
H
n
M
eCLT
,.
CCfeEgjAAUS
D GRC
(
a
Q
CHL
°J^JJa«i
^aWn^
""TfpRr
D
"C
D RWA
T3
«I
-0.2
D
-
D
CHE
D ARG
DZA,
1
o
MAR
MRT
D
BDI
JPN
D
1
I 2
fin
Lca«--"0 usa
SEQ
D
IDN
y = 0.1 083x- 0.5859
D C0G
R2 = 0.2224
BGO
a mus
-0.4
-
1
5
6.5
7
8
7.5
8.5
9
9.5
10
ln(Per Capita Income)
plots the standard deviation of the growth rate of real per capita income over the period 1960-97
against the log-level of average per capita GDP in 1985 PPP dollars over the same period. The bottom panel
plots the correlation of the growth rate of real per capita income growth with world average income growth
The top panel
excluding the country in question over the period 1960-97 against the log-level of average per capita
1985 PPP dollars over the same period. See Appendix for data definitions and sources.
48
GDP
in
Figure 2: Sample Paths of the Productivity Index
Country-Specific Variation Only
(11=0)
Time
Global Variation Only
0i=1)
Time
Both Country-Specific and Global Variation
(0<ii<1)
71
Time
Figure 3: Theoretical Volatility and
Volatility of
Comovement Graphs
Income Growth
Comovement of Income Growth
0.45
e=°oA=o
0.25
0.1
0.3
0.2
0.4
0.5
0.6
x
This figure plots Equations (14) and (15) as a function of x for the indicated values of 6 and X.
products
in
discussed
consumption
in
is
set equal to v=0.2
and the parameters
the text below.
50
of the productivity
The share
process are set as
of a-
—
Figure
Theoretical
4:
Volatility
Terms
Growth
of Trade
8=2A=0^5
-]
^^Z^f
0.02
=
.
0.015
of Trade
and Comovement Graphs
Volatility of
0.025
Terms
J
0.01
-
0.005
-
/^^^
^^^
/^^
^sf^
e=oo,X=0.35
"e^S
.
i
0.2
i
0.4
i
i
i
0.6
0.8
1
X
Comovement of Terms
of Trade
Growth
1.0
9=oo,X=0.35
0.5
0=2,^=0.35
0.0
o
/
o 2
0.4
0.8
0.6
e=2,a=o
-0.5
1
&=°°,\=o
-1.0
This figure plots Equations (17) and (18) as a function of x for the indicated values of 9 and X.
products
in
discussed
consumption
in
is
set equal to v=0.2
and the parameters
the text.
51
of the productivity
The share
process are set as
of
oc-
Figure
5: Volatility
and Comovement
Terms
of
of Trade
volatility
y = -6E-05x + 0.0232
0.07
0.06
R 2 = 2E-05
-|
ZAR
-
D
.c
GAB
s
o
H
o
to
1_
0.05
a
-
D COGD
D ZMB
D
8RA
LUX
ISL
ARG
0.04
-
D
1-
D
o
<n
E 0.03
-
DTGO
nB^
D ^a
1
U11U
D RWA D HTI
D NGA
D TCD
-
n
2
-
0.01
n
D
D
D
"•
,,,,„
MWI
CHL
cPeK. a
a
i
> 0.02
GUY
CAF
1—
55
D
ISR
PER
(
D
c
D
rjpNBSYi
D
^
,
««i
^i
TTO
ury
t|tvft
il.KQ?
Ba
i
a
slv
PRY D JAM
IRL
a^-SW
..
a
zaf
DEW
O MEX
nratft£ WE
esp
n «*"n MAR
Ca
„
Q BEN
EJ-i^M
D MDG D BGD
KEN
a
n
jpn
EK<BNK
atW,B AUS
a can
D USA
CHN
,
8
7.5
6.5
,
8.5
10
9.5
ln(Per Capita Income)
comovement
0.6
PHL
0.5
D
%
2
o
o>
T3
CO
(A
°
0.4
o
<u
Q-
C
E
o
I-
<u
D
0.2
0.1
TO
°
2
BDI
DBEN DQV
D
CAF
-I
D
D ZAO
a mwi
D
D
NER
TCD
D
NIC
™D^
SEN
D
NGA
°
IDN
a
S
n
D RWA
D
M
D ca
-0.1
-0.2
ZAF
MDG
0.3
-co.
o
D MYS n GRC
PEC3
E
O
u
n
isl
THA
2MB
D
URY
D
PRT
a
n
D
%w<.
u
a fin^
D FRA
R f&p
a
"^
ODjmS I^can
rft^E
^
JAM
cat? DZA
D ECU
NZL
isr
BEL
KCR
Q
a
a
CRI
ffifc4§ft>
n ARG
USA
BGD
mMAFY
MEX
° MRT
D
TTO
a
a mus
-0.3
che
= 0.01 39x + 0.0035
6.5
7.5
8
8.5
R
*M0056
:
10
ln(Per Capita Income)
plots the standard deviation of the growth rate of terms of trade over the period 1960-97 against
the log-level of average per capita GDP in 1985 PPP dollars over the same period. The bottom panel plots
the correlation of the growth rate of the terms of trade with world average income growth excluding the country
in question over the period 1960-97 against the log-level of average per capita GDP in 1985 PPP dollars over
the same period. See Appendix for data definitions and sources.
The top panel
52
Date Due
^
4/
^
Lib-26-67
MIT LIBRARIES
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