Comparative advantage and the cross-section of business cycles

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COMPARATIVE

ADVANTAGE

AND

THE

CROSS-SECTION

OF

BUSINESS

CYCLES

AartKraay JaunieVentura 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

AartKraay JaumeVentura 98-09 June, 1998

MASSACHUSETTS

INSTITUTE

OF

TECHNOLOGY

50

MEMORIAL

DRIVE

CAMBRIDGE,

MASS. 02142

MASSACHUSETTSINSTITUTE

OFTECHNOLOGY

SEP

1 6 1998

Comparative

Advantage

and

the

Cross-section

of

Business

Cycles

Aart

Kraay

Jaume

Ventura

The

World

Bank

M.I.T.

May,

1998

Abstract: Business cycles areboth less volatile

and

more

synchronizedwith the

world cycle in rich countriesthan in poorones. Inthis paper,

we

developtwo

alternative butnon-competing explanations forthese facts. Both explanations

proceed from the observation thatthelaw ofcomparative

advantage

causes

rich

and

poorcountriestospecialize inthe production ofdifferentcommodities. In particular, rich countriesspecialize in"high-tech"products

produced

byskilledworkerswhile

poorcountriesspecialize in "low-tech"products

produced

byunskilled workers. Cross-country differences inbusinesscyclesthen arise as a resultof

asymmetries

among

the industries in whichdifferentcountries specialize.

We

focus

on

two such asymmetries.

The

first

we

labelthe "competition bias" hypothesis,

and

is

based on

the ideathat cross-country differencesin production costsare

more

prevalent in

high-tech industries, sheltering producers fromforeign competition

and

therefore

making

them

large suppliers in the marketsfor theirproducts.

The

second

asymmetry

we

label the"cyclical bias" hypothesis,

and

is

based on

the ideathat production costs in

low-tech industriesmight

be

more

sensitivetothe shocks that drivebusinesscycles.

Commentsarewelcomeatakraay@worldbank.org(Kraay)andjaume@mit.edu (Ventura).Theviews

Businesscyclesare different in rich

and

poorcountries. Inthe top panelof

Figure 1,

we

have

plotted the standarddeviationof percapita

GDP

growthagainst

the log-level ofper capita

income

for

a

large

sample

of countries.

We

refer tothis

relationship astheVolatility

Graph

and

note thatitis downward-sloping,

meaning

that fluctuationsin percapita

income

growth are smallerin rich countries than in poor

ones. In the bottom panelof Figure 1,

we

have

plotted thecorrelation ofpercapita

income

growth rates with world

average

percapita

income

growth (excluding the

country in question) against thelog-level of percapita

income

forthe

same

setof

countries.

We

referto this relationship

as

the

Comovement

Graph

and

notethatit is

upward-sloping,

meaning

thatfluctuations inper capita

income

growth are

more

synchronizedwith the world cycle in rich countriesthan in poor ones. Table 1, which

isself-explanatory,

shows

thatthesefactsare quite robust.1

Here

we

developtwo alternative but non-competing explanationsfor these

facts. Both explanations rely

on

the notion thatthe lawof comparativeadvantage

causes

richcountries tospecialize in "high-tech" industries that require sophisticated

technologiesoperated

by

skilled workers, while poorcountriesspecializein "low-tech" industries that requiretraditional technologiesoperated byunskilledworkers. This

pattern of specialization

opens up

the possibilitythatcross-country differencesin

businesscycles are

due

to

asymmetries

between

high-tech

and

low-techindustries.

Forinstance,

assume

thatproduction inhigh-tech industries is

more

sensitiveto

foreign

shocks

and

less sensitive todomestic shocksthan in low-tech ones. Itfollows

immediatelythatproduction in high-tech industries,

and

therefore in rich countries,

would be more

synchronized with the world cycle than in low-tech ones. Moreover,to

the extentthatforeign

shocks

are

an average

ofthe domestic

shocks

of

many

other

countries, itis reasonableto expect thatforeign shocks areless volatile than

domesticshocks.

As

a

result, production in high-tech industries,

and

therefore in rich

countries,

would

also

be

less volatilethan in low-tech ones.

1

AcemogluandZilibotti(1997) also present theVolatilitygraph.

We

areunawareofanyprevious referencetotheComovementgraph.

One

explanation of

why

industries reactdifferentlyto shocks is

based on

the ideathatproducers in high-tech industriesenjoy

more

market

power

than producers

in low-tech industries.

We

referto this

asymmetry

among

industries asthe

"competition bias" hypothesis. This bias

would

occur, forinstance, if differences in

production costs

among

firms are

more

prevalentin high-tech industries.

These

cost

differences sheltertechnological leadersfrom theircompetitors

and

make

them

large suppliers in international markets.

This competition biashas implicationsfor

how

industries reacttodomestic

and

foreign shocks. Considerthe effects ofafavourabledomestic

shock

that reduces

unitcostsin all industries. Since producersin high-tech industriesare large suppliers

in international markets, increases in theirproduction lowerprices, moderating the

effects ofthe shock. Since producers in low-tech industriesare small suppliers in

world markets, increases in theirproduction

have

littleor noeffect

on

theirprices.

To

the extentthatthe competition biasis important,

one

would thereforeexpectthat

high-tech industries are less sensitiveto domesticshocksthan low-tech industries.

Considernext the effects of

a

foreign

shock

that raises production

and income

abroad and,as a result, increases

demand

in all industries. Since producers in

high-tech industriesare large suppliers in international markets, this

shock

istranslated

intoa large shift in theirindustry

demand

which leadsto large increases in production

and

prices. Since producers in low-tech industriesare small suppliers in international

markets, this

shock

has a negligible effect

on

their industry

demand

as

most

ofthe increase in world

demand

is

met

byincreases in production abroad.

To

the extent

thatthecompetition bias isimportant,

one would

therefore expectthat high-tech

industries are

more

sensitive toforeign shocksthan low-tech industries.

Anotherexplanation for

why

industries reactdifferentlyto

shocks

is

based on

theideathat unitcosts in the lattermight

be

more

sensitive tothe

shocks

thatdrive

businesscycles than inthe former.

We

referto this

asymmetry

among

industriesas

the"cyclicalbias" hypothesis. Ifbusiness cycles are driven byproductivityshocks,

business cycles are driven

by monetary

shocks, this bias mightarise if

cash-in-advance

constraints are

more

prevalentforfirms in low-tech industries.

This cyclical bias also has implicationsfor

how

industries reacttodomestic

and

foreign shocks. Almost by assumption, thecyclical bias implies that favourable

domesticshocks reduce unit costsin low-tech industries

more

than in high-tech

industries, leading tolargerincreases in production in theformerthan in the latter.

Thisis

how

the cyclical bias explains

why

high-tech industries areless sensitive to

domestic

shocks

than low-techindustries. Less obviously,the cyclical bias also

implies that high-tech industriesare

more

sensitive toforeign

shocks

than low-tech

industries.

To

see

this, considerthe effects ofa favourable

shock

that raises

production

and income

abroad.

The

cyclical bias implies thatworldwide productionof

low-tech products increases relative to thatof high-tech products, raisingthe relative

price ofhigh-tech products.

From

the perspective ofthe domestic

economy,

this

constitutes afavourable

shock

forproducersofhigh-tech products

and an

adverse

one

for low-tech producers.

As

a result, high-tech industriesare

more

sensitive to

foreign shocks than low-tech industries.

To

analyze these issues

we

constructastylizedworld equilibrium

model

of the cross-sectionofbusiness cycles. Inspired bythe

work

of Davis(1995),

we

consider a

world in which differences in bothfactor

endowments

a la Heckscher-Ohlin

and

industrytechnologies a la Ricardo

combine

todeterminea country'scomparative

advantage

and, therefore, the patternsof specialization

and

trade.

We

subjectthis

world

economy

toboth the sortof productivity fluctuations that

have

been

emphasized

by Kydland

and

Prescott(1982),

and

alsoto

monetary

shocks that

have

real effectssince firmsface cash-in-advanceconstraints.

We

then characterize the cross-section ofbusiness cycles

and

findconditions under whichthe competition

and

cyclical biases

can be

used

to explain the evidence in Figure 1.

The

model

issimple

enough

that

we

obtainclosed-form solutionsfor all the expressionsof interest.

We

alsofindthat ourresultshold

even

in the presence oftradefrictions, modelled here as"iceberg" transport costs, providedthatthesefrictionsare notso large asto alter

magnify cross-country differences in business cycles. Finally,

we

show

that thetwo hypotheses underconsideration

have

different implicationsfor thecyclical properties oftheterms oftrade. In principle, these properties

can be used

to distinguish

between

thetwo hypotheses. In practice, however, afirst look atthe datayields

conflicting evidence.

The

research presented here isrelatedtothe largeliterature

on

open-economy

real business cycle models, surveyed by Backus,

Kehoe

and

Kydland

(1995)

and

Baxter (1995), thatexplores

how

productivityshocks are transmitted

across countries.

Our work

also relates torecent

work

byObstfeld

and

Rogoff(1995,

1998)

and

Corsetti

and

Pesenti (1998) thatanalyzes theinternational transmissionof

monetary

shocks.

We

differfrom these lines ofresearch intwo ways. Insteadof

emphasizing theaspects in which businesscycles are similaracrosscountries,

we

focus

on

those aspects in whichthey are different. Instead offocusing primarily

on

the implications of international lending, risk-sharing

and

factor

movements

forthe transmission of businesscycles,

we

emphasize

the role of

commodity

trade.2

The

paperisorganized

as

follows. Section 1 develops the basicmodel.

Section

2

explores the properties ofa cross-section ofbusiness cycles in the basic

model. Section 3 extendsthe

model

byintroducing

money.

Section

4

furtherextends

the

model

byintroducingtransport costs. Section 5

examines

some

implications of

the

model

forcyclical properties oftheterms oftrade. Section 6concludes.

Previousliteratureonbusiness cyclesinopen economiestypicallyassumesthat either(a)thereisa

singlecommodity, sothatthereisno commoditytradewhatsoever,or(b)thatcountries arecompletely

specializedinthe productionofdifferentiated products. Whethersuchmodelsprovideagood

descriptionofobservedtrade patternshasnotbeen a major concernfor this literature. Incontrast,the

modelpresented hereisempiricallyconsistentwiththemainfeaturesofobservedtradepatterns: (a)a

largevolume oftradeamongrichcountriesinproductswith similar factor intensity (intraindustrytrade);

(b)substantialtradeamong richandpoorcountriesinproductswithdifferentfactor intensities

1.

A

Simple Model

of

Trade

and

Business

Cycles

We

consideraworldwith acontinuum ofcountrieswith

mass

one; two

industries, which

we

referto

as

the a-

and

p-industries;

and

two factors ofproduction,

skilled

and

unskilledworkers. Countriesdifferin theirtechnologies, their

endowments

ofskilled

and

unskilled workers

and

their level of productivity. In particular,

each

countryisdefined

by

atriplet (n,8,7i),

where

jj. isa

measure

of

how

advanced

the

technologyofthe countryis, 8isthe fraction ofthe populationthat is skilled,

and

n

is

an

indexofproductivity.

We

assume

thatworkers cannot migrate

and

that cross-country differences in technologyare stable, sothat)i

and

8are constant.

We

generate businesscycles byallowing the productivity index

n

to fluctuate randomly.

The

a-

and

p-industries

each

contain a continuum of differentiated productsof

measure one

which can

be

tradedat zero cost. Firms inthe a-industry use

sophisticated technologies that require skilledlabour, whilefirms in the p-industry use

traditional technologiesthat

can

be

operated byboth skilled

and

unskilledworkers.

Not surprisingly,

we

shall find that richcountries that

have

bettertechnologies

and

a

high proportion of skilledworkersexportmainlycc-products, whilepoor countriesthat

have

worse

technologies

and

a high proportion of unskilledworkers export mainly

p-products.

To

emphasize

the roleof

commodity

trade,

we

ruleout trade infinancial

instruments.

To

simplifythe problemfurther,

we

also ruleout investment. Jointly,

these assumptions implythat countries

do

notsave.3

Preferences

Each

country jspopulated by a continuum of

consumers

who

differin their level ofskills

and

theirpersonal opportunity cost ofwork, orreservation

wage.

We

3

index

consumers

by ie[1/y,00)

and

assume

thatthis index isdistributed accordingto this Pareto distribution: P(i)

=

1

-

(y•\)~

X

, with ?t>0,y>0.

A

consumer

with index i

maximizes

thefollowing expected utility:

E|U

ca(z,i) nV cp(i)

1-v

1-v K|) i \

e

-P-t.dt ₍₁₎ /

where

U(.) is

any

well-behavedfunction; l(i) is

an

indicatorfunction thattakes value 1

ifthe

consumer works and

otherwise;

and

ca(i)

and

c

p(i) are thefollowing

consumption indices ofa-

and

p-products:

c«(i)

=

e e

_

1 e-i _e-1 "•I e-i e-1

Jc

a(z,i) e dz cp(i)

=

Jcp(z,i) e -dz

_o

(2)

where

ca(z,i)

and

c_p(z,i)are

consumer

i'sconsumption ofvarietyzofthe a-

and

p-industries, respectively.

The

elasticity ofsubstitution

between

industries isone, while the elasticityofsubstitution

between any

twovarieties within

an

industry is9, with

e>i.

The

solution to theconsumer's problem isquite straightforward.

Consumers

spend

a fractionv oftheir

income on

a-products

and

afraction 1-v

on

p-products.

Moreover, the ratioofspending

on

any

twoa-products z

and

z' isgiven

by

Pa(z)

Pa(z')

1-e

;

and

the ratioofspending

on any

two p-productsz

and

z' is

Pp(z)

Pp(z') 1-e

where

pa(z)

and

_p

p(z)denote the price ofvarietyzofthe a-

and

p-products, respectively. Finally,

consumers work

if

and

onlyifthe applicable

wage

(skilled or

unskilled)

exceeds

a reservation

wage

of i" 1

V 1-v "1

Te

"1 1-e

Jp

a(z) 1-e -dz JPp(z) 1

-d2

.0 .0 j

We

expressall prices in termsof the ideal

consumer

price index, i.e.

=

1. Let r(p.,8,7i)

and

w(|j.,8,7t)

be

the

wages

of skilled

and

unskilled workers in a (p.,8,7i)-country. Also, define s(u.,8,7t)

and

u(u.,8,rc)

to

be

the

measure

ofskilled

and

unskilledworkers thatareemployed.

Under

the

assumptionthatthe distribution ofskills

and

reservation

wages

are independent,

we

have

that s

=

8-i r \ u

=

(1-6) ( \x i

w

\ 1 ) (3) (4)

Equations (3)-(4)

show

that thefraction ofskilled

and

unskilled workers thatare

employed

are f \x ' r ^ v lJ

and

'

w

'

y)

, respectively. Ifthe

wage

of

any

typeofworker

reachesy, theentire labour force ofthattype is

employed

and

the laboursupplyfor

that typeofworkers

becomes

vertical. Throughout,

we

shall

assume

thatyis large

enough

sothat thisnever happens. Finally,

we

notethatthe wage-elasticityofthe

laboursupplies, "k, isthe

same

forboth typesof workerssince itonly

depends on

the

dispersion of reservation

wages.

Firms

and Technology

The

oc-industry uses sophisticated production processesthatare not available

toall countries

and

thatrequire skilledworkers. Let

e~

ta

'n

dz (ea>0)

be

the

"best-practice" unitlabourrequirements to produce

one

unit ofa given small set of a-products of

measure

dz. Let (1

+

Ti)e

_£flc

'_n

technology available toproduce

one

unit ofa given small set ofa-products of

measure

dz. Let\i

be

the

measure

of a-products inwhich a firm located in a

(|a,8,7i)-country

owns

the best-practicetechnology.

We

can interpret u.a natural indicator of

how

advanced

thetechnology ofa countryis.

Assume

further that theset of

a-products in which two or

more

firms share best-practicetechnology has

measure

1 1

zero. Jointly, theseassumptions implythat 1

=

J Ju.

•dF(|j.,8),

where

F(u.,8) is the

oo

time-invariantjoint distribution function ofp.

and

8.

We

shall

assume

throughout that

ti is large

enough

so thatthefirms that

have

the best-practice technologyare'de

facto' monopolists in the marketfortheirproducts. Therefore, theiroptimal pricing policyis toset a

markup

overtheir unitcost.

Symmetry

ensuresthat that allfirms in

the a-industry ofa (ji,5,7i)-countrysetthe

same

price, _pa(p.,8,7i):

Pa=^r.e-

£_{« n}

(5)

The

p-industry usestraditional technologiesthat areavailable inall countries

and

can

be

operated byboth skilled

and

unskilledworkers. In particular,

e~

p n _-dz

(e_p>0)workersof

any

kind are requiredto produce

one

unit of

a

given "small"set of

p-products of

measure

dz. Since all firms

have

accesstothe

same

technologies, the

p-industryis competitive

and

pricesare equalto costs.

We

shall

assume

throughout

thatin equilibrium skilled

wages

are high

enough

thatonly unskilledworkers produce

P-products.4

Symmetry

ensures thatall firmsinthe p-industry of

a

(^,8,7i)-countryset

the

same

price, _p

p (n,8,7t):

Pp=w-e"

Epn (6)

Two

featuresof this _{representation oftechnologyplay}

_an

_{important role}

throughoutthe paper. First, theelasticity of substitution

among

varieties 6 regulates

the extentto whichthecompetition bias isimportant. If is low (high), a-products are

perceived

as

different(similar) by

consumers

and, as aresult, firms in the a-industry face

weak

(strong) competitionfrom producersofothervarieties ofa-products.

As

6->°°,the

degree

of competition in the a-industryincreases

and

the competition bias

disappears.

Second,

the parameters e„

and

e_p regulate the importanceofthe

cyclical bias. If ea<£p (£a>£p), unitcosts in the (3-industry (a-industry) are

more

sensitive to fluctuations in productivity.

As

£a->£p, the cyclical biasdisappears.

Productivity

Fluctuations

We

generate business cyclesby

assuming

that the productivityindex

fluctuatesrandomly. In particular,

we

assume

that

%

consists ofthe

sum

of a global

component,

n,

and a

country-specific

component,

n-Yl.

We

assume

thatthe global

and

country-specific

components

are independent,

and moreover

thatthe

country-specific

components

are independent across countries. Both the global

and

country-specific

components

of productivity are reflected Brownian motions

on

the

interval

n

n

2'2

, with zero drift

and

instantaneousvariances

odt

and

(1-o)dt

respectively,

where n

is

a

positiveconstant

and 0<a<1

.

These assumptions

imply

thatthe productivityindexitfollowsa

Brownian

motionwith zerodrift

and

unit

variance reflected

on

the interval

n-*,n

+

*

2 2

Thisinterval itselffluctuatesover

time

as

the global

component

ofproductivity changes. Finally, itis

a

well-known

resultofthe theoryofreflected Brownian motionthat the invariant distributionsofthe

global

and

country-specific

components

of productivity, G(IT)

and

G(7t-n), are uniform

on

theinterval

n

n

2'2

. 5

We

assume

thatthe initialcross-sectional distributionof

4

Thisisthecaseiftheshareofspendingona-productsnottoosmall, i.e.v»0.

5

thecountry-specific

component

ofproductivity is equal tothe invariantdistribution

and hence does

not

change

overtime.

From

the perspective ofa (u.,8,7t)-country,

we

can referto

changes

in n

and

n

as as domestic

and

foreign productivityshocks. Itisstraightforward to

show

thatthe

instantaneouscorrelation

between

these shocks is

Vo

7.

6

Thatis, the parameter

a

regulates the extenttowhichthe variation in domesticproductivity is

due

tothe global or country-specific components, i.e.

whether

it

comes

from

dn

or d(7t-n). Figure2

shows

possible

sample

pathsof

n

underthree differentassumptions regarding a. In

thefirstpanel,

we

assume

thato=0, sothat

n

isconstant

and

all the variation in

%

is country-specific.

The

second

panel

shows

thecase in which c=1. Then, djr=dn

and

all the variation in

n

is global, i.e.

changes

in

n

areperfectly correlatedwith

changes

in global productivity, n.

The

third panel

shows

the

case

inwhich

0<o<1

. Then, the

variation in

%

is has both country-specific

and

global

components.

Equilibrium Prices

and Trade Flows

Let_p

be

the average price of

an

oc-product(orthe ideal priceindex ofthe

cc-industry) relative totheaverage price ofa p-product product (orthe ideal price index

of the p-industry). Then,our normalization rule implies that

1 1 "1 1-e "1 1-e

Jp

a(z) 1-e -dz

=

_p1"v

and

Jp

p(z) 1-e -dz .0 .0

=

p v. Using this notation, the

equilibrium prices of

any

a-product

and

p-product

produced

ina (jj.,5,7t)-countryare:

Pa=X"P

1-v V-1 _1+A. 0+ *-.e e+x. e_{a (7t-n)} (7)

Thiswillbetrueexceptwheneithernor

n

arereflectedat theirrespective boundaries.Thesearerare

events sincethedatesatwhichthey occurconstituteasetofmeasurezerointhetimeline.

Pp

=

P

_V

(8)

where %

is a positiveconstant.7 Since

each

countryis a"large" producerof its

own

varieties of a-products, the price ofthese varieties

depends

negatively

on

the

quantity produced. Countries with

many

skilledworkers(high 5)with relatively high

productivity (high 71-n) producing

a

small

number

ofvarieties (lowp.) produce large

quantities of

each

varietyofthe a-products

and

as a result,face lowprices.

As

8->oo,

thedispersion in theirprices disappears

and

_pa

—

>p

1"v

. Inthe p-industry all products

must

command

the

same

price. Otherwise, low-price varieties of (3-products

would

not

be

produced

in equilibrium. Finally,

we

find thatthe equilibrium value for_p is:

p

=

vK-e

(e0"£a)'

n

(9)

where

\\fis anotherpositiveconstant.8 In the presenceofa cyclical bias,

e^ep

(£a>£p)» highproductivityisassociatedwith high (low) relative pricesfora-products as

theworldsupplyofp-products is high (low) relative tothat ofa-products.

As

_£a-»£p,

the cyclical biasdisappears

and

the relative prices ofboth industriesare unaffected

bythe level of productivity.

fi_i - 11 Tn^l e+x

(uT

(1+x)'e (7l_n)

7

Inparticular, _x = J JJji-

—

-e a dF(y,8)dG(jt-n),whichis

-~o o ^S_j

constant giventhatthedistributions Fand

G

aretime-invariant. To deriveEquation(7),equatetheratio ofworldexpenditureonthe(sum ofall)a-productsofa (u,5,7i)-countryand a(u',8',7t')-countrytotheratio ofthevalueofproductions. Second, use Equations(3)-(6) to find that:

P«' =Pre • •ee+^

a

. Finally,substitutethisexpression intheidealprice indexof

U-5'J

thecc-industryandsolvetor p„. Equation(8)issimplyaconsequenceofour normalization ruleandthe

observationthatallp-productscommandthesameprice inequilibrium.

1+1 R+i v ( e \x °° 11 (1+A.)-e R-(7i-n) 8 Inparticular, _\v v = J JJ(1-5) e p dF(u,8) dG(n- n) .

1-v

V.O-V

_^00

Toderive Equation(8),

we

equatetheratioofspendinginbothindustriestotheratioofworldwide productionofbothindustriesandthenuseEquations (3)-(7) tosolvefor p.

Lety(|a,5,7i;)

and

x(|i,8,7t)

be

the

income

and

theshare in production ofthe

a-r•s

industry, i.e.

y=rs+wu

and

x

=

. Notsurprisingly, countrieswith

good

technologies (high u.)

and

a high proportion of skilledworkers (high 5)

have

high

valuesforboth y

and

x.

We

therefore referto countrieswith high valuesofxasrich

countries. Since

each

country produces

an

infinitesimal

number

of varieties of

cc-products

and

consumes

allofthem, all countries exportalmostall of theirproduction

of a-products

and

import almostall oftheir

consumption

ofa-products.

As

a share of

income, theseexports

and

imports arex

and

v, respectively. This kind oftrade is usually referred toas intraindustry trade, since it involves

two-way

trade in products

with similar factorintensities.

To

balancetheirtrade, countrieswith

x<v

export

p-products

and

countrieswith x>v importthem.

As

a share ofincome, these exports

and

importsare v-x

and

x-v, respectively. Thiskind oftrade is usuallyreferred toas

interindustrytrade orfactor-proportions trade.

As

a result, the

model

captures in a stylized

manner

three broad empirical regularities regarding the patternsof trade: (a)

a large

volume

ofintraindustry trade

among

rich countries, (b) substantial

inter-industrytrade

between

rich

and

poorcountries,

and

(c) little trade

among

poor

countries.

2.

The

Cross-section

of

Business

Cycles

In theworld

economy

described in the previoussection, countriesare subject

totwo kinds ofshocks.

On

the

one

hand, domesticproductivityshocks shift industry supplies.

On

the other hand, foreign productivity

shocks

shiftindustry

demands.

In

the

presence

ofthe competition biasorthecyclical bias, theseshocks

have

different

effectsin high-tech

and

low-tech industries.

As

a result, the aggregate response to similar

shocks

differsacross

economies

with different industrial structures. Inother

words, the propertiesofthe businesscyclesthatcountriesexperience

depend

on

the

determinantsoftheir industrial structure, that is,

on

theirfactor

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 can

be

writtenas

a linearcombination ofdomestic

and

foreign shocks:9

dlny-E[dlny]

=

_^E

dn

+

^n

dn

(10)

The

functions ^(\i,8,n)

and

l,_n(\i.,b,n)

measure

thesensitivity ofa country's

growth rate todomestic

and

foreign shocks,

and

are givenby:

$K=<1 +

*.)-

xe

_f

9-1

Q

+ X

+

(1-x)-ep x'_e

«"rr^

+

(x

" v)(e

«

_e

_P) W

+

A (11) (12)

Toseethis,applyIto'slemmatothedefinition ofincome and usetheexpressionsforequilibrium factor

pricesandsuppliesinEquations(3)-(9).

Equations (10)-(12) providea completecharacterization ofthe businesscycles

experienced by a (ji,8,7t)-country. Moreover, they

show

how

business cycles differ

across countries, since thesensitivity ofgrowth ratesto domestic

and

foreign shocks

depends on

the share in production of high-tech products, x. Finally,

we

note the the

detrended growth rate ofworld average income, Y, is given by

dlnY-E[dlnY] =

co

_n

dn

(13)

where

the sensitivity oftheworld growth rate to innovations inthe global

component

of productivityis given by:

©n=(1

+

A.)-(v-e

_{a +(1-v):e}

p) (14)

LetV(u:,8,jt)denote the standard deviation ofthe growth rate ofa

(^1,8,71)-country,

and

letC(|i,8,7i) denotethe correlation of its growth ratewith world average

income

growth.

These

are thetheoretical analogsto theVolatility

and

Comovement

graphs in Figure 1. Using the Equations (10)-(14)

and

the properties ofthe shocks,

we

derive the following result:10

PROPOSITION

1:

The

functions

C

and

V

depend, at most,

on

x. Moreover:

(i)lf _£3

=£«•-—-,

then

—

=

—

=

for all x;

H

Q

+

X

dx dx

(ii) If en

>

e„ , then

——

<

and

——

>

forall x;

and

w

P a

e

+ X

dx dx

(iii) If e_R

<

e„ , then

-—

>

and

—

-

<

forall x.

w

+

A. 3x dx

10

Theproofissimple, since

we

haveclosed-formsolutionsforboth thevolatilityandcomovement

statistics: V =y(l-o)•Z,_{n +}a (t,_K +_£

_n

) and

C

= , . Since^+£_n

V(i-o)-§! +«•(£*

+Sn)

2

doesnotdependonx,V(C)willbedownward(upward) slopingifandonlyif

^

isdecreasingin x.The

propositiondescribesthe sign of for different parametervalues.

9x

This isthefirst ofa series of results that relate

a

country's industrial structure,

as

measured

byx,to the properties ofits business cycles. Proposition 1 says thatthe

theoretical Volatility

and

Comovement

graphs

have

the

same

slopes astheir

empirical counterparts if thecompetition bias (low8) and/orthecyclical bias (ep>£a)

are strongenough. Equations (11)-(12)

show

thatthis

same

parameter restriction

implies that rich countriesare less sensitive to domestic

shocks

(i.e. £,n is decreasing with x), but

more

sensitivetoforeign

shocks

(i.e. E,_n is increasing with x). In the

remainderofthis section

we

provide intuition for this result.

Why

Are

Rich Countries

Less

Sensitive

To

Domestic

Shocks?

Domestic shocks

shiftindustry supplies.

When

these shocks arepositive,

they raise production,

wages

and

employment

in both industries.

When

negative,

they lower production,

wages

and employment. However,

tothe extent thatthe

competition bias

and

the cyclical bias are important,these effectsare larger in the p-industrythanthe a-industry.

Itis useful tostartwith a

benchmark

case

in which 6->«>

and

Ea=Ep=£, sothat neitherthe competition bias nor thecyclical biasare present.

A

favourable

productivity

shock

results in

an

increase in productivity of

magnitude

e-drc in both

industries,

and

has twofamiliar effects. Holding constant

employment,

increased

productivity directlyraises production

and hence

income. This is nothing but the celebrated

Solow

residual

and

consistsofthe

sum

ofthe growth rates of productivity ofboth sectors, weighted bytheirsharesin production, i.e.e-drc. Increasedfactor productivityalso raisesthe

wages

ofskilled

and

unskilled workersand, as

a

result,

employment,

output

and income

risefurther. This contribution of

employment

growth

to thegrowth rateof

income

is

measured by

Xedm,

and

its strength

depends on

the

elasticityofthe laboursupply to

changes

in

wages,

X. Favourable domesticshocks

therefore raisegrowth rates in all countriesbythe

same

magnitude, i.e. (1+X)edn.

To

see

how

the competition bias determines

how

a countryreactsto domestic

shocks,

assume

thatG isfinite

and

ea=e_p=e.

As

in the

benchmark

case, favourable

domesticshocks raise productivity equally in the a-

and

p-industries, raising wages,

employment and

output. Thisiscaptured

by

the term (1+A.)-£-djtasbefore. However,

since thecountryis large in the marketsforitsa-products, increases in the supplyof

a-products are

met

with reductions in prices thatlower production

and

income. This

stabilizingeffectof prices is

measured by

the term

-x

•

^—

•e•drc.

The

more

9

+

A.

inelastic isthe

demand

facedby

each

cc-product (theloweris 0)

and

the larger is the

shareofthe a-industry (the larger isx), the

more

important isthisstabilizing roleof prices. Since rich countries

have

largercc-industries, domesticshocks

have

smaller

effects

on

theirgrowth rates, i.e. (1

+

X) 1

-

x •e•_drc

.

V, 9

+

KJ

To

see

how

the cyclicalbias determines

how

a countryrespondsto domestic

shocks,

assume

that0-»°<>

and

£c<ep.

Now

domestic

shocks

raise productivityin the a-industrybyEa-dic,

and

in the p-industry

by

fy-dn.

As

a result, both the

Solow

residual

and

the

employment

effectwill

be

smallerin the a-industry than in the

p-industry. Since richcountries

have

larger a-industries, domestic shocks

have

smaller

effects

on

theirgrowth rates, i.e. (1

+

a)•_[x e

a

+

(1

-

x)•epl-

dn

. Clearly, if_£a>£

P, the

conversewill

be

true.

To

sum

up, in all countries domesticproductivityshocks shiftoutwardsthe suppliesof a-

and

p-products. Since richcountries produce mainly high-tech products, they face inelastic industry

demands

(i.e. the competition bias)

and

experience relatively small shifts in supplies(i.e. the cyclical bias).

As

a

result, the

effectsofdomestic shocks

on income

are small in rich countries.

Poor

countries, by

virtueofproducingprimarily low-tech products, face elasticindustry

demands

and

experience relativelylarge shiftsin supplies.This is

why

the effects

on income

of

domestic shocksare large in poorcountries.

Why

Are

Rich Countries

More

Sensitive

to

Foreign

Shocks?

Foreign

shocks

shiftindustry

demands.

For instance, positive shocks raise

production

and income

in the restof theworld, increasing

demand

forall products.

Whether

this leadsto

an

increase inthe

demand

forthe domestic industry

depends

on

the extentto which the increase in

demand

is

met

by

an

increase in production

abroad.

To

the extentthatthe competition bias

and

the cyclical bias areimportant,

the increasein the

demand

for the a-industryisalways largerthan that ofthe

(3-industry.

It isuseful to start again with the

benchmark case

in which neitherthe

competition biasnor the cyclical biasare present, i.e. 9->«>

and

Ea=ep=e.

A

favourable

foreign

shock

consists of

an

increase in

average

productivity

abroad

of magnitude

edn

in both industries

and

therefore raisesworldwide

demand

and

production of

both a-

and

p-products.

However,

itfollowsfrom Equation (12) thatthis has

no

effect

inthe domestic

economy.

The

reason issimple

and

follows from threeassumptions.

First, the assumptionof homothetic preferencesensures that, atgiven prices, the

relative

demands

forboth typesof products are unaltered

as income

grows. Second,

the assumptionthat £a=£p ensuresthat, atgiven prices, the relative supplies ofboth

industriesare unaltered asproductivitygrows. Third, our assumption that 0->°°

ensuresthat

consumers

areverywillingto switchtheir

consumption

expenditures

over differentvarieties ofproducts.

The

firsttwo

assumptions

mean

thatthe increases in theforeignsupplies ofboth industries

match

exactly the increase in

demands

for bothindustries. Thisis

why

p

does

not

change

(recall Equation (9)).

The

third assumption

means

thatdespite the

change

in relative supplies ofdifferent

varieties of cc-products, there are

no changes

in their relativeprices.

To

see

how

the competition bias affects

how

a

country reacts to foreign

shocks,

assume

that9 isfinite

and

ea=ep=e. It isstilltrue that aftera favourable

foreign

shock

the increases in the foreign supplies of both industries

match

exactly

the increasein

demands

atthe industrylevel.

As

a resultp is not affected.

However,

since the increase in

demand

fordomestic cc-products is not

matched

by increased

production abroad, the price ofthesevarieties increases. This stimulates

wages,

employment and

production in the a-industry. Thiseffect is

measured

by

x•

—

•_{e drc}

,

and

is larger the

more

inelastic is the

demand

faced by

each

a-+

A,

product(the loweris6)

and

the largeris the share ofthe a-industry(the larger is x).

Since rich countries

have

larger a-industries, foreign shocks

have

larger effects

on

theirgrowth rates.

To

see

how

the cyclical bias determines

how

a country reactstoforeign

shocks,

assume

that 0->c»

and

ea<sp. At given prices,

we

have

now

thatafavourable

foreign

shock

raises theworld supplyofoc-products ((3-products) byless (more) than

its

demand.

As

a result, there is

an excess

demand

fora-products

and an

excess

supply ofp-products thatleadsto

an

increase in _p (recall Equation (9)).

From

the

pointofviewof thecountry, this is

an

increase inthe

demand

forthe domestic

cc-industry

and

a decrease in the

demand

forthe domestic (5-industry.

These

demand

shifts raise

wages,

employment and

production inthe a-industry,while lowering

them

in the (3-industry.

The

combined

effect in both industries is

measured

by

(1

+

A.)•(x

-

v)•fep

-

e

a)

and

its sign

depends on

whetherthecountry is a netexporter

ofa-or p-products. Since rich countries

have

larger a-industries, foreign shocks

have

larger effects

on

their growth rates.

To

sum

up,foreign

shocks

shiftthe

demands

ofboth industries at

home.

Since rich countries

have

a largershareofhigh-tech products, they

have

little

competitionfromforeign suppliers(i.e. the competition bias)

and

specializein industries

whose

prices

move

with the world cycle (i.e. the cyclical bias).

As

a result,

effectsofforeign shocksare positive

and

large. Poorcountriesproduce low-tech products and, as a result,face stiff competitionform abroad

and

specialize in

products

whose

price

moves

against the worldcycle.

As

a result, the effectsof foreignshocks are less positivethan in richcountries,

and

theymight

even be

negative.

The

Role

of

Commodity

Trade

In this model, the propertiesof businesscycles differacrosscountries

because

countries

have

different industrial structures, as

measured

by x.

There

are

many

determinants of the industrial structure ofa country.

We

focus here

on

perhaps

the

most

importantof such determinants, thatis,

a

country'sabilitytotrade. In fact, if

we

deny

this abilityto thecountriesthat populateourtheoretical world, their business

cycles

would

have

identical properties. Ina world ofautarky, x=v in every country

and

commodity

pricesare determined

by

domesticconditions. In such aworld the

sensitivities of growth rates to domestic

and

foreign shocks

would be

the

same

in all

countries,

_%^

=

(1

+

X) v•e

a

+

(1

-

v)•eg

and

^

=

;

and

the Volatility

and

Comovement

graphs

would

be

flat,

V

=(1

+

X)-C^Vc

7

.

V£

_a

+(1-V)£p

and

Moving

from aworld ofautarkyto a world offreetradeaffectsthe industrial

structure ofcountries since infreetradethe relative prices ofthose products in which

a countryhas comparative

advantage

are higher than in autarky. Higherpricesimply higher industryshares,

even

ifproduction remains constant. But

one would

also

expect higherprices tostimulate

employment and

production.

These

increases in

employment

could

come

from

unemployment,

as isthe case in the

model

presented

here.

Or

they could

come

from

employment

in otherindustries, as it

would

be

the

case

if

we

changed

ourassumptions

and

allowed both industriesto use bothtypesof

workers.

11

Thisresultdependsontheassumptionthattheelasticityofsubstitutionbetweena-productsand

p-productsisone. Otherwise, industrialstructureswouldalsobedifferentinautarkyandthecross-section

ofbusiness cycleswouldexhibitsomevariation.

3.

Monetary

Policy

In thissection

we

extend the

model

byintroducing

monetary

shocks as

an

additional source ofbusiness cyclesfluctuations.

As

is customaryin the literature

on

money

and

businesscycles,

we

assume

that

monetary

policy is erratic. This

simplificationis

adequate

if

one

takes the viewthat

monetary

policy hasobjectives

otherthanstabilizing thecycle. For instance, ifthe inflationtax is

used

to financea

publicgood, shockstothe marginal valueof thispublic

good

are translated into

shocks tothe rate of

money

growth. Alternatively, if

a

countryiscommitted to

maintaining afixed parity,

shocks

to foreign investors' confidence in the countryare

translated into shocksto the nominal interest rate,asthe

monetary

authoritiesuse

the latterto

manage

the

exchange

rate.

We

motivate the use of

money

by assuming

thatfirmsfacea

cash-in-advance

constraint.12 In particular, firms

have

to usecash in orderto

pay

a fraction of

their

wage

payments

before production starts. Firms borrowcash fromthe

government and

repaythe cash plusinterestafterproduction iscompleted

and

outputis soldtoconsumers.

Monetary

policyconsistsof settingthe interest rate

on

cash,

and

then distributing the

proceeds

orlosses ina

lump-sum

fashion

among

consumers. Increases inthe interest rate raise the financing costsoffirms, reducing

wages,

employment and

output. Inthis model, interest-rate shocks are therefore

formally equivalenttosupply

shocks such as changes

in production or payroll taxes.

The

Model

with

Money

Leti

be

theinterest rate

on

cash. Since

monetary

policyvaries across

countries,

each

countryis

now

defined by

a

quadruplet(n,8,7t,i).

We

constructthe

processforinterest-rate

shocks

followingthe

same

steps

we

used

to constructthe

12

SeeChristiano,Eichenbaum and Evans(1997)foradiscussionofrelatedmodels.

processfor productivity

shocks

in Section 1.

The

interest rateiconsists oftwo

independentpieces: a global

component,

I,

and

a country-specific

component,

i-I.

Moreover, the country-specific

components

are independent acrosscountries. Both

the global

component

and

the country-specific

components

of interestrates are

reflecting Brownian motions

on

the interval

i i

2'2

, with zerodrift

and

instantaneous variances<|>-dt

and

(1 -<J))dt respectively,

where

i is a positive constant

and

0<())<1.

These

assumptions

implythat the interest ratei isa Brownian motion

t l T l

2 2

The

initial

with zerodrift

and

unitvariance reflected

on

the interval

cross-sectional distribution ofthe country-specific

components,

H(i-I), is uniform

on

and hence does

not

change

overtime.

From

the perspective ofa

(u.,8,7i,i)-i i

2'2

country,

we

definedi

and

dlas domestic

and

foreign interest-rate shocks

and

note

thattheircorrelation coefficient

is^.

Finally, productivityshocks

and

interest-rate

shocks

are

assumed

to

be

independent.

The

introduction of

monetary

policy leads to minor

changes

in the equilibrium

ofthe model. Since cash-in-advance constraintsonlyaffectfirms, theconsumer's problem is notaltered

and

both thespending rules

and

the labour supplies in

Equations (3)-(4) remain valid. Regardingfirms,

we

assume

that

a

fraction of

wage

payments

k„

and

Kpinthe a-

and

p-industries

have

to

be

made

in

cash

before

production starts. Consequently, the costsof producinga small set ofproductsof

measure

dz includenot only the unitlabourrequirements,

e~

Za

'K

dz

and

e~

zV'n _{-dz, but also the financing costs, e}Ka

'

l

dz

and

eKpl-dz.13

As

a

result,

Equations (5)-(6)

have

to

be

replaced by:

p

a=

JL.

r

.e—

°

l

(15)

13

We

are usingthe followingapproximationshere: Ka-i^lnO+Ka-i)andKpi=ln(1+K Pi).

pp

=w-e

^

pl

(16)

An

interesting novelty ofthe

model

with

money

is that it indicatesanother

potential sourceforthe cyclical bias.

Even

if productivity is equallyvolatile in both

industries, i.e. £a=e_p, unitcosts could still

be more

volatile in the p-industry ifthe

cash-in-advance constraintis

more

bindingthere, Kp>K„. Finally,a straightforward

extension ofthe

arguments

in Section 1 can be

used

to

show

that Equation (8) isstill valid,while Equations (7)

and

(9)

must be

replaced by:14

Pa=x-P

1 -V

{fj

-e~

«*

₍₁₇₎ p

=

_¥

.e {ep-e_«

)n

-^

( ' Kp"

KjI

(18)

Equations (15)-(18)are natural generalizationsof Equations_{(5), (6),} (7)

and

(9).

As

the cash-in-advance constraints

become

less important, i.e. k^->0

and

Kp-»0,

this

model

convergesto the

model

without

money

presented in Section 1

.

Properties

of

Business

Cycles

With the additionof interest-rateshocks,

income

growth inthe

(|i,8,7i,i)-country is given bythisgeneralization of Equation (10):15

14

Theconstants%and\\tarenowgivenby:

X "₁

= J J

HH^

G

-

e8+X

'«*

V

_{.dF(^8).dG(K-n).dH(v-I)}

i+i o+i v ( e

^

co co 11 [(i+X)ER-(7t-n)-x-KB-(i-i)J

¥

i+ x x e+x = r b ; j JJ(1_6)._eV P P >*.dF0i.8).dG(7t-n).dH(i-i)

1-v

\?-V

^o-^rjO 15

To computeincome,rememberthat financingcosts arenotreallyacostfortheeconomyasa whole

butatransferfromfirmstoconsumersviathegovernment.

dlny-E[dlny]

=

^

d7c

+

_§

_n

dn-^

di-^

dl (19)

where

^(h,8,tc,i)

and

_£n(|-i,S,7t,i) arestill defined

by

Equations (11)-(12)

and

^(|j.,8,7t,i)

and

£,(11,8,71,1), which

measure

the sensitivityof

income

growth todomestic

and

foreign interest-rate shocks, are given by:

5i

=

\-e-1

XK„

_a Q

+

X

Si

=

1-1

+ 1

X-K„

_a Q

+ X

+

(1-X)Kp

(20) (21)

Equations (11)-(12)

and

(19)-(21) provide a complete characterizationof the

business cycles ofa (u.,8,7t,i)-country.

As

k^O

and

Kp->0,

we

have

that£,->0

and

£i->0

and

business cycles are driven onlybyproductivity shocks.

As

e„->0

and

Ep->0,

we

have

thatZ,K-^>0

and

i;n->0

and

businesscycles aredriven onlybyinterest-rate

shocks. In the general case,

however

businesscycles resultfromthe interaction of

both typeofshocks.

A

comparison

of (20)-(21)with (11)-(12) reveals thatthe effects ofdomestic

and

foreign

monetary

shocks

are verysimilartothoseof productivityshocks.

As

mentionedearlier, differences in the prevalenceofcash-in-advanceconstraints

provide

an

alternative sourceofcyclical bias, i.e. Ka

and

Kpplay the

same

role in (20)

and

(21)

as

e„

and

e_p

do

in (11)

and

(12). In contrastto productivityshocks, however,

monetary shocks

only

have

indirecteffects

on

production through theireffects

on

wages

and

laboursupplies. Therefore, thesensitivityof

income

growth to

monetary

shocks issmaller, i.e. theterm (1+X) which premultiplies (11)

and

(12) is replaced

with A,.

Since

we now

have

two sources ofbusiness cycles, world average growth is

given by:

dlnY-E[dlnY]

=

co_n

dn-(0[

dl (22)

where

con is still defined by Equation (14) while co, is given by:

a>

I

=A.-[v-K

+(1-v).Kp]

(23)

Ifproductivity

shocks

are negligible e_a=ep=0,

we

have

thefollowing result:

16

PROPOSITION

2:

The

functions

C

and

V

depend, at most,

on

x. Moreover:

(i) If k_r

= k„

, then

-—

=

——

=

forall x;

w

p a

Q

+

X

dx dx

(ii) If Kn

>

k„

, then

—

<

and

—

> forall x;

and

w

p a

Q

+

X

dx dx

(n) If kr

<

k„

, then

—

>

and

—

<

forall x.

p

Q

+ X

dx dx

Proposition 2 is the natural analogto Proposition 1 in aworld in which

business cycles are driven only byinterest-rate shocks.

The

competition

and

cyclical

biases

cause

cross-country differences in businesscycles, regardlessof

whether

the

cycles are driven by productivity

shocks

or interest-rate shocks.

The

intuition of

why

thecompetition bias

and

the cyclical bias generate these patternsina cross-section

ofbusiness cycles

has

been

discussed at length in Section2

and need

not

be

16

Notethatinthiscase

v-j[i-.).{?,..(

t,.{,)

i!

M

dc..

kMM

r

TheproofisanalogoustothatofProposition 1

.

repeated here. Instead,

we

generalize Propositions 1

and

2 tothe case

where

both

productivity shocks

and

interest rate

shocks

drive businesscycles, asfollows:17

av

PROPOSITION

3:

The

functions

C

and

V

depend, atmost,

on

x. Moreover, if

—

<

3x (

—

>0),

then

—

>0

(—

<0).

Define: 3x 3x 3x ? (

0-1

"\ ? (

6-1

^

A

= (1-a)-0+*r-|e

o

-Q^-epJ-ep+(1-*)-*

-I

K

_a

-^-^-K

p

J-Kp

;

B

=

(1-c).(1

+

X)2

{e„.^I-e

p)

+

(l-«.»?

.(«.

.£!-«,

J

Then,

(i) IfA>0,

—

>

forall x;

3x

(iij if-B<A<0,

—

<0

(—

>0)

if

x<--

(x>--);and

3x dx

B

B

(iii) ifA<-B, then

—

<

forall x.

3x

Proposition3 provides

a

set of necessary

and

sufficient conditionsforthe functions

V

and

C

to exhibitthe

same

slopesthantheirempirical counterparts. Let x*

be

the highestvaluefor xin a cross-section ofcountries.Then, a necessary

and

sufficientcondition forbusinesscyclesto

be

lessvolatile

and

more

synchronized with

theworld cycle in rich countries isthat

A+Bx*<0.

Thiscondition isalwayssatisfied if

bothtypesof

shocks

generate industry responseswith the rightbiases, i.e.

17

Notethat

V

=

^(1-c)-^

+

a-£

_n +_Sn)2

+(1-4>K?

+4>-(Si +Sl)

2

and

a-«>n"ten +Sn> +*-

m

_i-($i-HJi)

C

= Sinceneither

y(o-o>ft

+**»?)-((1-oK|

+o(U

+S

n

)

2

+(1-4>K

2

+<MSi

+^i)

2

)

2 2

^,,+^nnor %,+tndependonx,

V

(C) isdownward (upward)slopingifandonlyif (1-o)-i,_{n +}(1-<t>)

• %x isdecreasing(increasing) in x.Thepropositiondescribes thesignof

—

1(1-o)•Z,_{n +}(1-<|>)•

£,

x Ifor

3xv '

differentparametervalues.

£r

>

En

and

Kn

>

k„

. Butthis is nota necessarycondition. For

instance, itmight bethatthe cc-industryis

more

sensitive todomestic productivity

(interest-rate)shocks

and

lesssensitive to foreign productivity (interest-rate)shocks

6—1

6—1

than the (3-industry, £r

<

e_a (kr

< K

a -), yetstill business cycles are

6

+

A, 6

+

A.

less volatile

and

more

synchronized with theworld cycle in rich countries. This

naturallyrequiresthatthe cc-industry

be

less sensitive todomesticinterest-rate (productivity)shocks

and

more

sensitive toforeign interest-rate (productivity)shocks,

6-1

,

6-1

,

K

P

>K

a

-—

(ep

>e

a

-

—

).

4.

Trade

Integration

The

postwarperiod has

seen

large reductionsin both physical

and

policy

barriers to

commodity

trade.

Here

we

do

notattemptto explain these

changes

but instead explore

how

parametric reductions in transport costsaffectthe cross-section

ofbusiness cycles. Throughout,

we

assume

that transportcostsare small

enough

relativeto cross-country differences in factor

endowments

that all countries areeither

netimporters or netexporters ofthe p-product, for

any

value oftheirdomestic

productivity

and

interest rates,

and

forall possible equilibrium prices. Moreover,

we

assume

thattransportcosts are small

enough

relative tocross-country differences in

technologyin the a-industrythateverya-product continuesto

be

produced

in only

one

country.

These

assumptions ensure thatthe pattern oftrade is

unchanged

bythe

introduction oftransport costs, although the

volume

oftrade is negatively relatedto

the size of transportcosts.

Remember

thatthe

main

theme

of this

paper

is thatthe nature ofbusiness

cycles

a

country experiences

depends on

its industrial structure.

As

transport costs

decline, the pricesofproducts inwhich a countryhas comparative

advantage

increaseand, as a result,the share in productionofthese industries increases.

A

naturalconclusion ofthis

argument

is that

one

should expectthatreductionsin

transportcosts (globalization?) increase the cross-countryvariation inthe properties

ofbusiness cycles.

We

confirm this intuition here.

The

Model

with

Transport

Costs

We

generalize the

model

with

money

by

assuming

thattrade incurs transport

costsofthe "iceberg"variety, i.e. ift>1 units ofoutput are shipped across borders,

only

one

unitarrives at the destinationwhilex-1 units "melt" in transit. Let p«(z)

and

Pp(z)

now

denote thef.o.b. or international price of variety zofthe a-products

and

of

the p-products, respectively.

We

use the

same

normalization rule

as

before in terms of theseinternational prices,

and

define p as asthe

average

f.o.b. price ofa-products

relative to p-products.

The

presenceof transportcosts implies thatthe c.i.f. or

domestic product prices varyacrosscountries. In

each

country, the c.i.f. prices of

imports

and

import-competing products are higher than thef.o.b. priceswhile the

c.i.f. prices ofexports are equal tothef.o.b. prices. Since countries importall the

varieties ofa-products they

do

not produce, the c.i.f. price ofall but the infinitesimal

measure

u.ofdomestically-produced a-products is x- _pa(z). Similarly, thec.i.f. price of

P-products is xpp(z) ifthe country is

a

net importerof p-products,

and

_pp(z)

otherwise.

Note thatthe

consumer

continuesto allocate

consumption

expenditures

(evaluated atc.i.f. prices) overcommodities exactlyasbefore.

The

consumer's

laboursupply decision is also

unchanged:

consumers work

if

and

only ifthe

applicable

wage,

expressed in termsof a unitofconsumption,

exceeds

their

reservation

wage. However,

since

consumers

located in differentcountriesface

differentc.i.f. prices, theprice of a unitof

consumption

now

variesacross countries.

Let_pc(n,8,rc,i) denotethe ideal price indexof

consumption

in

a

(u.,8,7r,i)-country. This

indexisgiven byxifthe countryis a net importerofthe p-product,

and

xvotherwise.18 Therefore,

we

need

to replace Equations (3)-(4) bythefollowinggeneralizations:

r s

=

5-( r ^

YPc

(

w

> u

=

(1-8)-

-?-U-Pcy

(24) X (25) 18

Toseethis,usethenormalizationruleandrecallthatallcountriesimportallbut theinfinitesmal

numberofa-productsproduceddomestically,andsoincurrthetransportcoston(almost)theirentire

consumptionofa-products,whichconstituteafractionvoftotalexpenditure. Inaddition,consumersin

countries thatarenetimportersofp-productsfaceac.i.f.priceofxp

pfor theirremaining expenditureon

P-products.

Since a-productsare exported in all countries, producers face identical c.i.f.

and

f.o.b. prices and, as a result, Equation (15) isstill valid.

However,

Equation (16)

isonlyvalid in countriesthat export p-products. In countries thatimport p-products, the producer price oftheseproducts isT-p_p, and,

as

a result, Equation (16) hasto

be

replaced by: T-p p

=w-e"

E P-7C+KPl (26)

Straightforward but

somewhat

tedious algebra revealsthatthe expressions

for equilibrium pricesin Equations (8), (17)

and

(18) still hold, provided that

we

replace 8

and

1-8with 8•x~

x

and

x•₍₁

-

_{8) if}thecountry _is a net importer_of

p-products,

and

with 5-t

4v

and

(1-8)-t~*"v otherwise.19

Whiletrade patternsare unchanged, the world

economy

with transport costs

exhibits lesscross-countryvariation in industrialstructures than the world

economy

with free trade.

The

higher the transport costs are, the loweristhe price ofthose

industries inwhich thecountry has comparative advantage. Thatis, the loweris the price of a-products (P-products) in rich (poor) countries. Forthe reasons

mentioned

before,this leads to

an

reduction inthe share ofthecc-industry (P-industry) in rich

(poor) countries.20

19

ToderivetheanalogtoEquation(17),

we

can equatethe ratioofworldexpenditureonthe(sumofall)

a-productsinany twocountriestothe ratioof the valueofproductionsasbefore. Usingthenew

expressionsforwagesintheexpressionsforfactorsuppliesresultsin

1 (..,<! -A.

Wi

1+x .. /- „M x Pa' =

Pa

u'-6 _p

C

H-6p

_c

, Q+X

^•

e_a-(*-n,

)-77r

Ka-(i-i')

•eH+K 1 A . Insertingthisintheideal priceindex

forthe a-industryyieldsthe appropriatemodificationofEquation (17). Equation(8) issimplya

consequenceofourunchangednormalizationrule.ToobtaintheanalogtoEquation (18),notefirstthat thepresenceoftransportcostsimplies thatthemarket-clearingconditionsinthea-andp-lndustries

cannowbe expressed asequating the valueofworld productionatproducerprices tothevalueofworld

consumptionatconsumerpricesforalla-andp-products.Then, using the analogtoEquation (17),the

newexpressionsforfactor prices,andthe factorsupplieswecan equatetheratioofexpenditureinboth

industriestothe ratioofproductionsatproducerpricestoobtainthe appropriate modificationof (18).

20

Itisstraightforward toverify thisbysubstitutingtheexpressionsforequilibriumwages and

employmentintothedefinitionofxanddifferentiatingwith respecttox.

Business

Cycles

and

Transport

Costs

The

(demeaned)

growth rate of

income

isstill given by Equations (11)-(12)

and

(19)-(21). Consequently, Proposition 3 relatingthe properties of businesscycles

toa country'sindustrial structure still holds.

However,

transportcosts reducethe

volume

oftrade and, as a result, the cross-sectional dispersion inx.This implies that

thecross-section of businesscycles exhibits less variation in the

model

with transport

coststhan in the free-trademodel.

A

processof parametric reductionsintransportcosts

has

opposite effects

on

the business cyclesof rich

and

poorcountries. Ifthecompetition

and

cyclical biases

are important,

we

know

thatthe Volatility

and

Comovement

graphs are

downward

and

upward

slopingwith x, respectively. Therefore, reductions intransport costs

lowerthe volatilityofbusinesscycles in rich countries (as theirx increases)

and

raise

volatility in poorcountries (astheirx decreases). Similarly, reductions intransport

costs

make

business cycles

more

synchronized with theworld cycle in rich countries

(astheirx increases)

and

less synchronized with theworld cycle inpoorcountries(as

theirxdecreases).