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COMPARATIVE
ADVANTAGE
AND
THE
CROSSSECTION
OF
BUSINESS
CYCLES
AartKraay JaunieVentura 9809 June,1998
massachusetts
institute
of
technology
50
memorial
drive
Cambridge,
mass. 02139
WORKING
PAPER
DEPARTMENT
OF
ECONOMICS
COMPARATIVE
ADVANTAGE
AND
THE
CROSSSECTION
OF
BUSINESS
CYCLES
AartKraay JaumeVentura 9809 June, 1998
MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
50
MEMORIAL
DRIVE
CAMBRIDGE,
MASS. 02142
MASSACHUSETTSINSTITUTE
OFTECHNOLOGY
SEP
1 6 1998Comparative
Advantage
and
the
Crosssection
of
Business
Cycles
Aart
Kraay
Jaume
Ventura
The
World
Bank
M.I.T.May,
1998
Abstract: Business cycles areboth less volatile
and
more
synchronizedwith theworld cycle in rich countriesthan in poorones. Inthis paper,
we
developtwoalternative butnoncompeting explanations forthese facts. Both explanations
proceed from the observation thatthelaw ofcomparative
advantage
causes
richand
poorcountriestospecialize inthe production ofdifferentcommodities. In particular, rich countriesspecialize in"hightech"products
produced
byskilledworkerswhilepoorcountriesspecialize in "lowtech"products
produced
byunskilled workers. Crosscountry differences inbusinesscyclesthen arise as a resultofasymmetries
among
the industries in whichdifferentcountries specialize.We
focuson
two such asymmetries.The
firstwe
labelthe "competition bias" hypothesis,and
isbased on
the ideathat crosscountry differencesin production costsare
more
prevalent inhightech industries, sheltering producers fromforeign competition
and
thereforemaking
them
large suppliers in the marketsfor theirproducts.The
second
asymmetry
we
label the"cyclical bias" hypothesis,
and
isbased on
the ideathat production costs inlowtech industriesmight
be
more
sensitivetothe shocks that drivebusinesscycles.Commentsarewelcomeatakraay@worldbank.org(Kraay)andjaume@mit.edu (Ventura).Theviews
Businesscyclesare different in rich
and
poorcountries. Inthe top panelofFigure 1,
we
have
plotted the standarddeviationof percapitaGDP
growthagainstthe loglevel ofper capita
income
fora
largesample
of countries.We
refer tothisrelationship astheVolatility
Graph
and
note thatitis downwardsloping,meaning
that fluctuationsin percapitaincome
growth are smallerin rich countries than in poorones. In the bottom panelof Figure 1,
we
have
plotted thecorrelation ofpercapitaincome
growth rates with worldaverage
percapitaincome
growth (excluding thecountry in question) against theloglevel of percapita
income
forthesame
setofcountries.
We
referto this relationshipas
theComovement
Graph
and
notethatit isupwardsloping,
meaning
thatfluctuations inper capitaincome
growth aremore
synchronizedwith the world cycle in rich countriesthan in poor ones. Table 1, which
isselfexplanatory,
shows
thatthesefactsare quite robust.1Here
we
developtwo alternative but noncompeting explanationsfor thesefacts. Both explanations rely
on
the notion thatthe lawof comparativeadvantagecauses
richcountries tospecialize in "hightech" industries that require sophisticatedtechnologiesoperated
by
skilled workers, while poorcountriesspecializein "lowtech" industries that requiretraditional technologiesoperated byunskilledworkers. Thispattern of specialization
opens up
the possibilitythatcrosscountry differencesinbusinesscycles are
due
toasymmetries
between
hightechand
lowtechindustries.Forinstance,
assume
thatproduction inhightech industries ismore
sensitivetoforeign
shocks
and
less sensitive todomestic shocksthan in lowtech ones. Itfollowsimmediatelythatproduction in hightech industries,
and
therefore in rich countries,would be more
synchronized with the world cycle than in lowtech ones. Moreover,tothe extentthatforeign
shocks
arean average
ofthe domesticshocks
ofmany
othercountries, itis reasonableto expect thatforeign shocks areless volatile than
domesticshocks.
As
a
result, production in hightech industries,and
therefore in richcountries,
would
alsobe
less volatilethan in lowtech ones.1
AcemogluandZilibotti(1997) also present theVolatilitygraph.
We
areunawareofanyprevious referencetotheComovementgraph.One
explanation ofwhy
industries reactdifferentlyto shocks isbased on
the ideathatproducers in hightech industriesenjoymore
marketpower
than producersin lowtech industries.
We
referto thisasymmetry
among
industries asthe"competition bias" hypothesis. This bias
would
occur, forinstance, if differences inproduction costs
among
firms aremore
prevalentin hightech industries.These
costdifferences sheltertechnological leadersfrom theircompetitors
and
make
them
large suppliers in international markets.This competition biashas implicationsfor
how
industries reacttodomesticand
foreign shocks. Considerthe effects ofafavourabledomesticshock
that reducesunitcostsin all industries. Since producersin hightech industriesare large suppliers
in international markets, increases in theirproduction lowerprices, moderating the
effects ofthe shock. Since producers in lowtech industriesare small suppliers in
world markets, increases in theirproduction
have
littleor noeffecton
theirprices.To
the extentthatthe competition biasis important,
one
would thereforeexpectthathightech industries are less sensitiveto domesticshocksthan lowtech industries.
Considernext the effects of
a
foreignshock
that raises productionand income
abroad and,as a result, increases
demand
in all industries. Since producers inhightech industriesare large suppliers in international markets, this
shock
istranslatedintoa large shift in theirindustry
demand
which leadsto large increases in productionand
prices. Since producers in lowtech industriesare small suppliers in internationalmarkets, this
shock
has a negligible effecton
their industrydemand
as
most
ofthe increase in worlddemand
ismet
byincreases in production abroad.To
the extentthatthecompetition bias isimportant,
one would
therefore expectthat hightechindustries are
more
sensitive toforeign shocksthan lowtech industries.Anotherexplanation for
why
industries reactdifferentlytoshocks
isbased on
theideathat unitcosts in the lattermightbe
more
sensitive totheshocks
thatdrivebusinesscycles than inthe former.
We
referto thisasymmetry
among
industriesasthe"cyclicalbias" hypothesis. Ifbusiness cycles are driven byproductivityshocks,
business cycles are driven
by monetary
shocks, this bias mightarise ifcashinadvance
constraints aremore
prevalentforfirms in lowtech industries.This cyclical bias also has implicationsfor
how
industries reacttodomesticand
foreign shocks. Almost by assumption, thecyclical bias implies that favourabledomesticshocks reduce unit costsin lowtech industries
more
than in hightechindustries, leading tolargerincreases in production in theformerthan in the latter.
Thisis
how
the cyclical bias explainswhy
hightech industries areless sensitive todomestic
shocks
than lowtechindustries. Less obviously,the cyclical bias alsoimplies that hightech industriesare
more
sensitive toforeignshocks
than lowtechindustries.
To
see
this, considerthe effects ofa favourableshock
that raisesproduction
and income
abroad.The
cyclical bias implies thatworldwide productionoflowtech products increases relative to thatof hightech products, raisingthe relative
price ofhightech products.
From
the perspective ofthe domesticeconomy,
thisconstitutes afavourable
shock
forproducersofhightech productsand an
adverseone
for lowtech producers.As
a result, hightech industriesaremore
sensitive toforeign shocks than lowtech industries.
To
analyze these issueswe
constructastylizedworld equilibriummodel
of the crosssectionofbusiness cycles. Inspired bythework
of Davis(1995),we
consider aworld in which differences in bothfactor
endowments
a la HeckscherOhlinand
industrytechnologies a la Ricardo
combine
todeterminea country'scomparativeadvantage
and, therefore, the patternsof specializationand
trade.We
subjectthisworld
economy
toboth the sortof productivity fluctuations thathave
been
emphasized
by Kydlandand
Prescott(1982),and
alsotomonetary
shocks thathave
real effectssince firmsface cashinadvanceconstraints.
We
then characterize the crosssection ofbusiness cyclesand
findconditions under whichthe competitionand
cyclical biases
can be
used
to explain the evidence in Figure 1.The
model
issimpleenough
thatwe
obtainclosedform solutionsfor all the expressionsof interest.We
alsofindthat ourresultshold
even
in the presence oftradefrictions, modelled here as"iceberg" transport costs, providedthatthesefrictionsare notso large asto altermagnify crosscountry differences in business cycles. Finally,
we
show
that thetwo hypotheses underconsiderationhave
different implicationsfor thecyclical properties oftheterms oftrade. In principle, these propertiescan be used
to distinguishbetween
thetwo hypotheses. In practice, however, afirst look atthe datayieldsconflicting evidence.
The
research presented here isrelatedtothe largeliteratureon
openeconomy
real business cycle models, surveyed by Backus,Kehoe
and
Kydland(1995)
and
Baxter (1995), thatexploreshow
productivityshocks are transmittedacross countries.
Our work
also relates torecentwork
byObstfeldand
Rogoff(1995,1998)
and
Corsettiand
Pesenti (1998) thatanalyzes theinternational transmissionofmonetary
shocks.We
differfrom these lines ofresearch intwo ways. Insteadofemphasizing theaspects in which businesscycles are similaracrosscountries,
we
focus
on
those aspects in whichthey are different. Instead offocusing primarilyon
the implications of international lending, risksharing
and
factormovements
forthe transmission of businesscycles,we
emphasize
the role ofcommodity
trade.2The
paperisorganizedas
follows. Section 1 develops the basicmodel.Section
2
explores the properties ofa crosssection ofbusiness cycles in the basicmodel. Section 3 extendsthe
model
byintroducingmoney.
Section4
furtherextendsthe
model
byintroducingtransport costs. Section 5examines
some
implications ofthe
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 ofcountrieswithmass
one; twoindustries, which
we
refertoas
the aand
pindustries;and
two factors ofproduction,skilled
and
unskilledworkers. Countriesdifferin theirtechnologies, theirendowments
ofskilled
and
unskilled workersand
their level of productivity. In particular,each
countryisdefined
by
atriplet (n,8,7i),where
jj. isameasure
ofhow
advanced
thetechnologyofthe countryis, 8isthe fraction ofthe populationthat is skilled,
and
n
isan
indexofproductivity.We
assume
thatworkers cannot migrateand
that crosscountry differences in technologyare stable, sothat)iand
8are constant.We
generate businesscycles byallowing the productivity index
n
to fluctuate randomly.The
aand
pindustrieseach
contain a continuum of differentiated productsofmeasure one
which canbe
tradedat zero cost. Firms inthe aindustry usesophisticated technologies that require skilledlabour, whilefirms in the pindustry use
traditional technologiesthat
can
be
operated byboth skilledand
unskilledworkers.Not surprisingly,
we
shall find that richcountries thathave
bettertechnologiesand
ahigh proportion of skilledworkersexportmainlyccproducts, whilepoor countriesthat
have
worse
technologiesand
a high proportion of unskilledworkers export mainlypproducts.
To
emphasize
the roleofcommodity
trade,we
ruleout trade infinancialinstruments.
To
simplifythe problemfurther,we
also ruleout investment. Jointly,these assumptions implythat countries
do
notsave.3Preferences
Each
country jspopulated by a continuum ofconsumers
who
differin their level ofskillsand
theirpersonal opportunity cost ofwork, orreservationwage.
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 imaximizes
thefollowing expected utility:EU
ca(z,i) nV cp(i)1v
1v K) i \e
Pt.dt _{(1)} /where
U(.) isany
wellbehavedfunction; l(i) isan
indicatorfunction thattakes value 1ifthe
consumer works and
otherwise;and
ca(i)and
cp(i) are thefollowing
consumption indices ofa
and
pproducts:c«(i)
=
e e
_
1 ei _{e1} "•I ei e1
Jc
a(z,i) e dz cp(i)=
Jcp(z,i) e dz_o
(2)
where
ca(z,i)and
c_{p}(z,i)areconsumer
i'sconsumption ofvarietyzofthe aand
pindustries, respectively.
The
elasticity ofsubstitutionbetween
industries isone, while the elasticityofsubstitutionbetween any
twovarieties withinan
industry is9, withe>i.
The
solution to theconsumer's problem isquite straightforward.Consumers
spend
a fractionv oftheirincome on
aproductsand
afraction 1von
pproducts.Moreover, the ratioofspending
on
any
twoaproducts zand
z' isgivenby
Pa(z)
Pa(z')
1e
;
and
the ratioofspendingon any
two pproductszand
z' isPp(z)
Pp(z') 1e
where
pa(z)and
_{p}p(z)denote the price ofvarietyzofthe a
and
pproducts, respectively. Finally,consumers work
ifand
onlyifthe applicablewage
(skilled orunskilled)
exceeds
a reservationwage
of i" 1V 1v "1
Te
"1 1eJp
a(z) 1e dz JPp(z) 1d2
.0 .0 jWe
expressall prices in termsof the idealconsumer
price index, i.e.=
1. Let r(p.,8,7i)and
w(j.,8,7t)be
thewages
of skilled
and
unskilled workers in a (p.,8,7i)country. Also, define s(u.,8,7t)and
u(u.,8,rc)to
be
themeasure
ofskilledand
unskilledworkers thatareemployed.Under
theassumptionthatthe distribution ofskills
and
reservationwages
are independent,we
have
that s=
8i r \ u=
(16) ( \x iw
\ 1 ) (3) (4)Equations (3)(4)
show
that thefraction ofskilledand
unskilled workers thatareemployed
are f \x ' r ^ v lJand
'w
'y)
, respectively. Ifthe
wage
ofany
typeofworkerreachesy, theentire labour force ofthattype is
employed
and
the laboursupplyforthat typeofworkers
becomes
vertical. Throughout,we
shallassume
thatyis largeenough
sothat thisnever happens. Finally,we
notethatthe wageelasticityofthelaboursupplies, "k, isthe
same
forboth typesof workerssince itonlydepends on
thedispersion of reservation
wages.
Firms
and Technology
The
ocindustry uses sophisticated production processesthatare not availabletoall countries
and
thatrequire skilledworkers. Lete~
ta'n
dz (ea>0)
be
the"bestpractice" unitlabourrequirements to produce
one
unit ofa given small set of aproducts ofmeasure
dz. Let (1+
Ti)e_£flc
'_{n}
technology available toproduce
one
unit ofa given small set ofaproducts ofmeasure
dz. Let\ibe
themeasure
of aproducts inwhich a firm located in a(a,8,7i)country
owns
the bestpracticetechnology.We
can interpret u.a natural indicator ofhow
advanced
thetechnology ofa countryis.Assume
further that theset ofaproducts in which two or
more
firms share bestpracticetechnology hasmeasure
1 1
zero. Jointly, theseassumptions implythat 1
=
J Ju.
•dF(j.,8),
where
F(u.,8) is theoo
timeinvariantjoint distribution function ofp.
and
8.We
shallassume
throughout thatti is large
enough
so thatthefirms thathave
the bestpractice technologyare'defacto' monopolists in the marketfortheirproducts. Therefore, theiroptimal pricing policyis toset a
markup
overtheir unitcost.Symmetry
ensuresthat that allfirms inthe aindustry ofa (ji,5,7i)countrysetthe
same
price, _{p}a(p.,8,7i):Pa=^r.e
£_{« n}(5)
The
pindustry usestraditional technologiesthat areavailable inall countriesand
canbe
operated byboth skilledand
unskilledworkers. In particular,e~
p n _{dz}(e_{p}>0)workersof
any
kind are requiredto produceone
unit ofa
given "small"set ofpproducts of
measure
dz. Since all firmshave
accesstothesame
technologies, thepindustryis competitive
and
pricesare equalto costs.We
shallassume
throughoutthatin equilibrium skilled
wages
are highenough
thatonly unskilledworkers producePproducts.4
Symmetry
ensures thatall firmsinthe pindustry ofa
(^,8,7i)countrysetthe
same
price, _{p}p (n,8,7t):
Pp=we"
Epn (6)Two
featuresof this _{representation} _{of}_{technology}_{play}_{an}
_{important} _{role}throughoutthe paper. First, theelasticity of substitution
among
varieties 6 regulatesthe extentto whichthecompetition bias isimportant. If is low (high), aproducts are
perceived
as
different(similar) byconsumers
and, as aresult, firms in the aindustry faceweak
(strong) competitionfrom producersofothervarieties ofaproducts.As
6>°°,the
degree
of competition in the aindustryincreasesand
the competition biasdisappears.
Second,
the parameters e„and
e_{p} regulate the importanceofthecyclical bias. If ea<£p (£a>£p), unitcosts in the (3industry (aindustry) are
more
sensitive to fluctuations in productivity.
As
£a>£p, the cyclical biasdisappears.Productivity
Fluctuations
We
generate business cyclesbyassuming
that the productivityindexfluctuatesrandomly. In particular,
we
assume
that%
consists ofthesum
of a globalcomponent,
n,and a
countryspecificcomponent,
nYl.We
assume
thatthe globaland
countryspecificcomponents
are independent,and moreover
thatthecountryspecific
components
are independent across countries. Both the globaland
countryspecific
components
of productivity are reflected Brownian motionson
theinterval
n
n
2'2
, with zero driftand
instantaneousvariancesodt
and
(1o)dtrespectively,
where n
isa
positiveconstantand 0<a<1
.These assumptions
implythatthe productivityindexitfollowsa
Brownian
motionwith zerodriftand
unitvariance reflected
on
the intervaln*,n
+
*
2 2
Thisinterval itselffluctuatesover
time
as
the globalcomponent
ofproductivity changes. Finally, itisa
wellknownresultofthe theoryofreflected Brownian motionthat the invariant distributionsofthe
global
and
countryspecificcomponents
of productivity, G(IT)and
G(7tn), are uniformon
theintervaln
n
2'2
. 5We
assume
thatthe initialcrosssectional distributionof4
Thisisthecaseiftheshareofspendingonaproductsnottoosmall, i.e.v»0.
5
thecountryspecific
component
ofproductivity is equal tothe invariantdistributionand hence does
notchange
overtime.From
the perspective ofa (u.,8,7t)country,we
can refertochanges
in nand
n
as as domestic
and
foreign productivityshocks. Itisstraightforward toshow
thattheinstantaneouscorrelation
between
these shocks isVo
7.6
Thatis, the parameter
a
regulates the extenttowhichthe variation in domesticproductivity is
due
tothe global or countryspecific components, i.e.whether
itcomes
fromdn
or d(7tn). Figure2shows
possiblesample
pathsofn
underthree differentassumptions regarding a. Inthefirstpanel,
we
assume
thato=0, sothatn
isconstantand
all the variation in%
is countryspecific.The
second
panelshows
thecase in which c=1. Then, djr=dnand
all the variation in
n
is global, i.e.changes
inn
areperfectly correlatedwithchanges
in global productivity, n.
The
third panelshows
thecase
inwhich0<o<1
. Then, thevariation in
%
is has both countryspecificand
globalcomponents.
Equilibrium Prices
and Trade Flows
Let_{p}
be
the average price ofan
ocproduct(orthe ideal priceindex oftheccindustry) relative totheaverage price ofa pproduct product (orthe ideal price index
of the pindustry). Then,our normalization rule implies that
1 1 "1 1e "1 1e
Jp
a(z) 1e dz=
_{p}1"vand
Jp
p(z) 1e dz .0 .0=
p v. Using this notation, theequilibrium prices of
any
aproductand
pproductproduced
ina (jj.,5,7t)countryare:Pa=X"P
1v V1 _{1+A.} 0+ *.e e+x. e_{a (7tn)} (7)Thiswillbetrueexceptwheneithernor
n
arereflectedat theirrespective boundaries.Thesearerareevents sincethedatesatwhichthey occurconstituteasetofmeasurezerointhetimeline.
Pp
=
P_V
(8)where %
is a positiveconstant.7 Sinceeach
countryis a"large" producerof itsown
varieties of aproducts, the price ofthese varieties
depends
negativelyon
thequantity produced. Countries with
many
skilledworkers(high 5)with relatively highproductivity (high 71n) producing
a
smallnumber
ofvarieties (lowp.) produce largequantities of
each
varietyofthe aproductsand
as a result,face lowprices.As
8>oo,thedispersion in theirprices disappears
and
_{p}a—
>p1"v
. Inthe pindustry all products
must
command
thesame
price. Otherwise, lowprice varieties of (3productswould
not
be
produced
in equilibrium. Finally,we
find thatthe equilibrium value for_{p} is:p
=
vKe(e0"£a)'
n
(9)
where
\\fis anotherpositiveconstant.8 In the presenceofa cyclical bias,e^ep
(£a>£p)» highproductivityisassociatedwith high (low) relative pricesforaproducts as
theworldsupplyofpproducts is high (low) relative tothat ofaproducts.
As
_{£a»£p,}the cyclical biasdisappears
and
the relative prices ofboth industriesare unaffectedbythe 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(jtn),whichis~o o ^S_{j}
constant giventhatthedistributions Fand
G
aretimeinvariant. To deriveEquation(7),equatetheratio ofworldexpenditureonthe(sum ofall)aproductsofa (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
U5'J
theccindustryandsolvetor p„. Equation(8)issimplyaconsequenceofour normalization ruleandthe
observationthatallpproductscommandthesameprice inequilibrium.
1+1 R+i v ( e \x °° 11 (1+A.)e R(7in) 8 Inparticular, _{\v} v = J JJ(15) e p dF(u,8) dG(n n) .
1v
V.OV
_{^00}
Toderive Equation(8),
we
equatetheratioofspendinginbothindustriestotheratioofworldwide productionofbothindustriesandthenuseEquations (3)(7) tosolvefor p.Lety(a,5,7i;)
and
x(i,8,7t)be
theincome
and
theshare in production ofthear•s
industry, i.e.
y=rs+wu
and
x=
. Notsurprisingly, countrieswithgood
technologies (high u.)
and
a high proportion of skilledworkers (high 5)have
highvaluesforboth y
and
x.We
therefore referto countrieswith high valuesofxasrichcountries. Since
each
country producesan
infinitesimalnumber
of varieties ofccproducts
and
consumes
allofthem, all countries exportalmostall of theirproductionof aproducts
and
import almostall oftheirconsumption
ofaproducts.As
a share ofincome, theseexports
and
imports arexand
v, respectively. This kind oftrade is usually referred toas intraindustry trade, since it involvestwoway
trade in productswith similar factorintensities.
To
balancetheirtrade, countrieswithx<v
exportpproducts
and
countrieswith x>v importthem.As
a share ofincome, these exportsand
importsare vxand
xv, respectively. Thiskind oftrade is usuallyreferred toasinterindustrytrade orfactorproportions trade.
As
a result, themodel
captures in a stylizedmanner
three broad empirical regularities regarding the patternsof trade: (a)a large
volume
ofintraindustry tradeamong
rich countries, (b) substantialinterindustrytrade
between
richand
poorcountries,and
(c) little tradeamong
poorcountries.
2.
The
Crosssection
of
Business
Cycles
In theworld
economy
described in the previoussection, countriesare subjecttotwo kinds ofshocks.
On
theone
hand, domesticproductivityshocks shift industry supplies.On
the other hand, foreign productivityshocks
shiftindustrydemands.
Inthe
presence
ofthe competition biasorthecyclical bias, theseshockshave
differenteffectsin hightech
and
lowtech industries.As
a result, the aggregate response to similarshocks
differsacrosseconomies
with different industrial structures. Inotherwords, the propertiesofthe businesscyclesthatcountriesexperience
depend
on
thedeterminantsoftheir industrial structure, that is,
on
theirfactorendowments
and
technology.
Domestic
and
Foreign
Shocks
as
a
Source
ofBusiness
Cycles
The
(demeaned)
growth rate ofincome
in a (n.,8,7i)country canbe
writtenasa linearcombination ofdomestic
and
foreign shocks:9dlnyE[dlny]
=
_{^}_{E}dn
+
^n
dn
(10)The
functions ^(\i,8,n)and
l,_{n}(\i.,b,n)measure
thesensitivity ofa country'sgrowth rate todomestic
and
foreign shocks,and
are givenby:$K=<1 +
*.)xe
_{f}91
Q+ X
+
(1x)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 differacross countries, since thesensitivity ofgrowth ratesto domestic
and
foreign shocksdepends on
the share in production of hightech products, x. Finally,we
note the thedetrended growth rate ofworld average income, Y, is given by
dlnYE[dlnY] =
co_{n}
dn
(13)where
the sensitivity oftheworld growth rate to innovations inthe globalcomponent
of productivityis given by:
©n=(1
+
A.)(ve_{a +(1v):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 averageincome
growth.These
are thetheoretical analogsto theVolatilityand
Comovement
graphs in Figure 1. Using the Equations (10)(14)
and
the properties ofthe shocks,we
derive the following result:10PROPOSITION
1:The
functionsC
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 ae
+ X
dx dx(iii) If e_{R}
<
e„ , then—
>
and
—
<
forall x.w
+
A. 3x dx10
Theproofissimple, since
we
haveclosedformsolutionsforboth thevolatilityandcomovementstatistics: V =y(lo)•Z,_{n +}a (t,_{K} +_{£}
_{n}
) and
C
= , . Since^+£_{n}V(io)§! +«•(£*
+Sn)
2
doesnotdependonx,V(C)willbedownward(upward) slopingifandonlyif
^
isdecreasingin x.Thepropositiondescribesthe 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 thatthetheoretical Volatility
and
Comovement
graphshave
thesame
slopes astheirempirical counterparts if thecompetition bias (low8) and/orthecyclical bias (ep>£a)
are strongenough. Equations (11)(12)
show
thatthissame
parameter restrictionimplies that rich countriesare less sensitive to domestic
shocks
(i.e. £,n is decreasing with x), butmore
sensitivetoforeignshocks
(i.e. E,_{n} is increasing with x). In theremainderofthis 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 thatthecompetition bias
and
the cyclical bias are important,these effectsare larger in the pindustrythanthe aindustry.Itis useful tostartwith a
benchmark
case
in which 6>«>and
Ea=Ep=£, sothat neitherthe competition bias nor thecyclical biasare present.A
favourableproductivity
shock
results inan
increase in productivity ofmagnitude
edrc in bothindustries,
and
has twofamiliar effects. Holding constantemployment,
increasedproductivity directlyraises production
and hence
income. This is nothing but the celebratedSolow
residualand
consistsofthesum
ofthe growth rates of productivity ofboth sectors, weighted bytheirsharesin production, i.e.edrc. Increasedfactor productivityalso raisesthewages
ofskilledand
unskilled workersand, asa
result,employment,
outputand income
risefurther. This contribution ofemployment
growthto thegrowth rateof
income
ismeasured by
Xedm,
and
its strengthdepends on
theelasticityofthe laboursupply to
changes
inwages,
X. Favourable domesticshockstherefore raisegrowth rates in all countriesbythe
same
magnitude, i.e. (1+X)edn.To
seehow
the competition bias determineshow
a countryreactsto domesticshocks,
assume
thatG isfiniteand
ea=e_{p}=e.As
in thebenchmark
case, favourabledomesticshocks raise productivity equally in the a
and
pindustries, raising wages,employment and
output. Thisiscapturedby
the term (1+A.)£djtasbefore. However,since thecountryis large in the marketsforitsaproducts, increases in the supplyof
aproducts are
met
with reductions in prices thatlower productionand
income. Thisstabilizingeffectof prices is
measured by
the termx
•^—
•e•drc.
The
more
9
+
A.inelastic isthe
demand
facedbyeach
ccproduct (theloweris 0)and
the larger is theshareofthe aindustry (the larger isx), the
more
important isthisstabilizing roleof prices. Since rich countrieshave
largerccindustries, domesticshockshave
smallereffects
on
theirgrowth rates, i.e. (1+
X) 1
x •e•_{drc}.
V, 9
+
KJTo
seehow
the cyclicalbias determineshow
a countryrespondsto domesticshocks,
assume
that0»°<>and
£c<ep.Now
domesticshocks
raise productivityin the aindustrybyEadic,and
in the pindustryby
fydn.As
a result, both theSolow
residual
and
theemployment
effectwillbe
smallerin the aindustry than in thepindustry. Since richcountries
have
larger aindustries, domestic shockshave
smallereffects
on
theirgrowth rates, i.e. (1+
a)•_{[x} ea
+
(1
x)•epldn
. Clearly, if_{£a>£}P, the
conversewill
be
true.To
sum
up, in all countries domesticproductivityshocks shiftoutwardsthe suppliesof aand
pproducts. Since richcountries produce mainly hightech products, they face inelastic industrydemands
(i.e. the competition bias)and
experience relatively small shifts in supplies(i.e. the cyclical bias).
As
a
result, theeffectsofdomestic shocks
on income
are small in rich countries.Poor
countries, byvirtueofproducingprimarily lowtech products, face elasticindustry
demands
and
experience relativelylarge shiftsin supplies.This is
why
the effectson income
ofdomestic shocksare large in poorcountries.
Why
Are
Rich Countries
More
Sensitive
toForeign
Shocks?
Foreign
shocks
shiftindustrydemands.
For instance, positive shocks raiseproduction
and income
in the restof theworld, increasingdemand
forall products.Whether
this leadstoan
increase inthedemand
forthe domestic industrydepends
on
the extentto which the increase indemand
ismet
byan
increase in productionabroad.
To
the extentthatthe competition biasand
the cyclical bias areimportant,the increasein the
demand
for the aindustryisalways largerthan that ofthe(3industry.
It isuseful to start again with the
benchmark case
in which neitherthecompetition biasnor the cyclical biasare present, i.e. 9>«>
and
Ea=ep=e.A
favourableforeign
shock
consists ofan
increase inaverage
productivityabroad
of magnitudeedn
in both industriesand
therefore raisesworldwidedemand
and
production ofboth a
and
pproducts.However,
itfollowsfrom Equation (12) thatthis hasno
effectinthe domestic
economy.
The
reason issimpleand
follows from threeassumptions.First, the assumptionof homothetic preferencesensures that, atgiven prices, the
relative
demands
forboth typesof products are unalteredas 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 switchtheirconsumption
expendituresover differentvarieties ofproducts.
The
firsttwoassumptions
mean
thatthe increases in theforeignsupplies ofboth industriesmatch
exactly the increase indemands
for bothindustries. Thisiswhy
pdoes
notchange
(recall Equation (9)).The
third assumption
means
thatdespite thechange
in relative supplies ofdifferentvarieties of ccproducts, there are
no changes
in their relativeprices.To
see
how
the competition bias affectshow
a
country reacts to foreignshocks,
assume
that9 isfiniteand
ea=ep=e. It isstilltrue that aftera favourableforeign
shock
the increases in the foreign supplies of both industriesmatch
exactlythe increasein
demands
atthe industrylevel.As
a resultp is not affected.However,
since the increase in
demand
fordomestic ccproducts is notmatched
by increasedproduction abroad, the price ofthesevarieties increases. This stimulates
wages,
employment and
production in the aindustry. Thiseffect ismeasured
byx•
—
•_{e} _{drc},
and
is larger themore
inelastic is thedemand
faced byeach
a+
A,product(the loweris6)
and
the largeris the share ofthe aindustry(the larger is x).Since rich countries
have
larger aindustries, foreign shockshave
larger effectson
theirgrowth rates.
To
see
how
the cyclical bias determineshow
a country reactstoforeignshocks,
assume
that 0>c»and
ea<sp. At given prices,we
have
now
thatafavourableforeign
shock
raises theworld supplyofocproducts ((3products) byless (more) thanits
demand.
As
a result, there isan excess
demand
foraproductsand an
excesssupply ofpproducts thatleadsto
an
increase in _{p} (recall Equation (9)).From
thepointofviewof thecountry, this is
an
increase inthedemand
forthe domesticccindustry
and
a decrease in thedemand
forthe domestic (5industry.These
demand
shifts raisewages,
employment and
production inthe aindustry,while loweringthem
in the (3industry.
The
combined
effect in both industries ismeasured
by(1
+
A.)•(x
v)•fep
ea)
and
its signdepends on
whetherthecountry is a netexporterofaor pproducts. Since rich countries
have
larger aindustries, foreign shockshave
larger effectson
their growth rates.To
sum
up,foreignshocks
shiftthedemands
ofboth industries athome.
Since rich countries
have
a largershareofhightech products, theyhave
littlecompetitionfromforeign suppliers(i.e. the competition bias)
and
specializein industrieswhose
pricesmove
with the world cycle (i.e. the cyclical bias).As
a result,effectsofforeign shocksare positive
and
large. Poorcountriesproduce lowtech products and, as a result,face stiff competitionform abroadand
specialize inproducts
whose
pricemoves
against the worldcycle.As
a result, the effectsof foreignshocks are less positivethan in richcountries,and
theymighteven be
negative.
The
Role
ofCommodity
Trade
In this model, the propertiesof businesscycles differacrosscountries
because
countrieshave
different industrial structures, asmeasured
by x.There
aremany
determinants of the industrial structure ofa country.We
focus hereon
perhapsthe
most
importantof such determinants, thatis,a
country'sabilitytotrade. In fact, ifwe
deny
this abilityto thecountriesthat populateourtheoretical world, their businesscycles
would
have
identical properties. Ina world ofautarky, x=v in every countryand
commodity
pricesare determinedby
domesticconditions. In such aworld thesensitivities of growth rates to domestic
and
foreign shockswould be
thesame
in allcountries,
_{%^}
=
(1+
X) v•ea
+
(1
v)•egand
^
=
;
and
the Volatilityand
Comovement
graphswould
be
flat,V
=(1+
X)C^Vc
7.
V£
_{a}
+(1V)£p
and
Moving
from aworld ofautarkyto a world offreetradeaffectsthe industrialstructure 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. Butone would
alsoexpect higherprices tostimulate
employment and
production.These
increases inemployment
couldcome
fromunemployment,
as isthe case in themodel
presentedhere.
Or
they couldcome
fromemployment
in otherindustries, as itwould
be
thecase
ifwe
changed
ourassumptionsand
allowed both industriesto use bothtypesofworkers.
11
Thisresultdependsontheassumptionthattheelasticityofsubstitutionbetweenaproductsand
pproductsisone. Otherwise, industrialstructureswouldalsobedifferentinautarkyandthecrosssection
ofbusiness cycleswouldexhibitsomevariation.
3.
Monetary
Policy
In thissection
we
extend themodel
byintroducingmonetary
shocks asan
additional source ofbusiness cyclesfluctuations.
As
is customaryin the literatureon
money
and
businesscycles,we
assume
thatmonetary
policy is erratic. Thissimplificationis
adequate
ifone
takes the viewthatmonetary
policy hasobjectivesotherthanstabilizing thecycle. For instance, ifthe inflationtax is
used
to financeapublicgood, shockstothe marginal valueof thispublic
good
are translated intoshocks tothe rate of
money
growth. Alternatively, ifa
countryiscommitted tomaintaining afixed parity,
shocks
to foreign investors' confidence in the countryaretranslated into shocksto the nominal interest rate,asthe
monetary
authoritiesusethe latterto
manage
theexchange
rate.We
motivate the use ofmoney
by assuming
thatfirmsfaceacashinadvance
constraint.12 In particular, firmshave
to usecash in ordertopay
a fraction oftheir
wage
payments
before production starts. Firms borrowcash fromthegovernment and
repaythe cash plusinterestafterproduction iscompletedand
outputis soldtoconsumers.
Monetary
policyconsistsof settingthe interest rateon
cash,
and
then distributing theproceeds
orlosses inalumpsum
fashionamong
consumers. Increases inthe interest rate raise the financing costsoffirms, reducing
wages,
employment and
output. Inthis model, interestrate shocks are thereforeformally equivalenttosupply
shocks such as changes
in production or payroll taxes.The
Model
with
Money
Leti
be
theinterest rateon
cash. Sincemonetary
policyvaries acrosscountries,
each
countryisnow
defined bya
quadruplet(n,8,7t,i).We
constructtheprocessforinterestrate
shocks
followingthesame
stepswe
used
to constructthe12
SeeChristiano,Eichenbaum and Evans(1997)foradiscussionofrelatedmodels.
processfor productivity
shocks
in Section 1.The
interest rateiconsists oftwoindependentpieces: a global
component,
I,and
a countryspecificcomponent,
iI.Moreover, the countryspecific
components
are independent acrosscountries. Boththe global
component
and
the countryspecificcomponents
of interestrates arereflecting Brownian motions
on
the intervali i
2'2
, with zerodriftand
instantaneous variances<>dt
and
(1 <J))dt respectively,where
i is a positive constantand
0<())<1.These
assumptions
implythat the interest ratei isa Brownian motiont l T l
2 2
The
initialwith zerodrift
and
unitvariance reflectedon
the intervalcrosssectional distribution ofthe countryspecific
components,
H(iI), is uniformon
and hence does
notchange
overtime.From
the perspective ofa(u.,8,7i,i)i i
2'2
country,
we
definediand
dlas domesticand
foreign interestrate shocksand
notethattheircorrelation coefficient
is^.
Finally, productivityshocksand
interestrateshocks
areassumed
tobe
independent.The
introduction ofmonetary
policy leads to minorchanges
in the equilibriumofthe model. Since cashinadvance constraintsonlyaffectfirms, theconsumer's problem is notaltered
and
both thespending rulesand
the labour supplies inEquations (3)(4) remain valid. Regardingfirms,
we
assume
thata
fraction ofwage
payments
k„and
Kpinthe aand
pindustrieshave
tobe
made
incash
beforeproduction 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
eKpldz.13As
a
result,Equations (5)(6)
have
tobe
replaced by:p
a=
JL.
r.e—
°l
(15)
13
We
are usingthe followingapproximationshere: Kai^lnO+Kai)andKpi=ln(1+K Pi).pp
=we
^
pl(16)
An
interesting novelty ofthemodel
withmoney
is that it indicatesanotherpotential sourceforthe cyclical bias.
Even
if productivity is equallyvolatile in bothindustries, i.e. £a=e_{p}, unitcosts could still
be more
volatile in the pindustry ifthecashinadvance constraintis
more
bindingthere, Kp>K„. Finally,a straightforwardextension ofthe
arguments
in Section 1 can beused
toshow
that Equation (8) isstill valid,while Equations (7)and
(9)must be
replaced by:14Pa=xP
1 V{fj
e~
«*
_{(17)} p=
_{¥}
.e {epe_{«})n
^
( ' Kp"KjI
(18)Equations (15)(18)are natural generalizationsof Equations_{(5), (6),} (7)
and
(9).
As
the cashinadvance constraintsbecome
less important, i.e. k^>0and
Kp»0,this
model
convergesto themodel
withoutmoney
presented in Section 1.
Properties
ofBusiness
Cycles
With the additionof interestrateshocks,
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(Kn).dH(vI)}i+i o+i v ( e
^
co co 11 [(i+X)ER(7tn)xKB(ii)J¥
i+ x x e+x = r b ; j JJ(1_6)._{e}V P P >*.dF0i.8).dG(7tn).dH(ii)1v
\?V
^o^rjO 15To computeincome,rememberthat financingcosts arenotreallyacostfortheeconomyasa whole
butatransferfromfirmstoconsumersviathegovernment.
dlnyE[dlny]
=
^
d7c+
_{§}_{n}
dn^
di^
dl (19)where
^(h,8,tc,i)and
_{£}n(i,S,7t,i) arestill definedby
Equations (11)(12)and
^(j.,8,7t,i)and
£,(11,8,71,1), whichmeasure
the sensitivityofincome
growth todomesticand
foreign interestrate shocks, are given by:
5i
=
\e1
XK„
_{a} Q+
X
Si=
11+ 1
XK„
_{a} Q+ X
+
(1X)Kp
(20) (21)Equations (11)(12)
and
(19)(21) provide a complete characterizationof thebusiness cycles ofa (u.,8,7t,i)country.
As
k^O
and
Kp>0,we
have
that£,>0and
£i>0
and
business cycles are driven onlybyproductivity shocks.As
e„>0and
Ep>0,we
have
thatZ,K^>0and
i;n>0and
businesscycles aredriven onlybyinterestrateshocks. In the general case,
however
businesscycles resultfromthe interaction ofboth typeofshocks.
A
comparison
of (20)(21)with (11)(12) reveals thatthe effects ofdomesticand
foreignmonetary
shocks
are verysimilartothoseof productivityshocks.As
mentionedearlier, differences in the prevalenceofcashinadvanceconstraintsprovide
an
alternative sourceofcyclical bias, i.e. Kaand
Kpplay thesame
role in (20)and
(21)as
e„and
e_{p}do
in (11)and
(12). In contrastto productivityshocks, however,monetary shocks
onlyhave
indirecteffectson
production through theireffectson
wages
and
laboursupplies. Therefore, thesensitivityofincome
growth tomonetary
shocks issmaller, i.e. theterm (1+X) which premultiplies (11)
and
(12) is replacedwith A,.
Since
we now
have
two sources ofbusiness cycles, world average growth isgiven by:
dlnYE[dlnY]
=
co_{n}dn(0[
dl (22)where
con is still defined by Equation (14) while co, is given by:a>
I
=A.[vK
+(1v).Kp]
(23)Ifproductivity
shocks
are negligible e_{a}=ep=0,we
have
thefollowing result:16
PROPOSITION
2:The
functionsC
and
V
depend, at most,on
x. Moreover:(i) If k_{r}
= k„
, then—
=
——
=
forall x;w
p aQ
+
X
dx dx(ii) If Kn
>
k„
, then—
<
and
—
> forall x;and
w
p aQ
+
X
dx dx(n) If kr
<
k„
, then—
>
and
—
<
forall x.p
Q
+ X
dx dxProposition 2 is the natural analogto Proposition 1 in aworld in which
business cycles are driven only byinterestrate shocks.
The
competitionand
cyclicalbiases
cause
crosscountry differences in businesscycles, regardlessofwhether
thecycles are driven by productivity
shocks
or interestrate shocks.The
intuition ofwhy
thecompetition biasand
the cyclical bias generate these patternsina crosssectionofbusiness cycles
has
been
discussed at length in Section2and need
notbe
16
Notethatinthiscase
vj[i.).{?,..(
t,.{,)i!
M
dc..
kMM
r
TheproofisanalogoustothatofProposition 1
.
repeated here. Instead,
we
generalize Propositions 1and
2 tothe casewhere
bothproductivity shocks
and
interest rateshocks
drive businesscycles, asfollows:17av
PROPOSITION
3:The
functionsC
and
V
depend, atmost,on
x. Moreover, if—
<
3x (
—
>0),
then—
>0
(—
<0).
Define: 3x 3x 3x ? (01
"\ ? (61
^A
= (1a)0+*re
o
Q^epJep+(1*)*
IK
_{a}^^K
pJKp
;B
=
(1c).(1+
X)2{e„.^Ie
p)+
(l«.»?
.(«..£!«,
J
Then,(i) IfA>0,
—
>
forall x;3x
(iij ifB<A<0,
—
<0
(—
>0)
ifx<
(x>);and
3x dx
B
B
(iii) ifA<B, then
—
<
forall x.3x
Proposition3 provides
a
set of necessaryand
sufficient conditionsforthe functionsV
and
C
to exhibitthesame
slopesthantheirempirical counterparts. Let x*be
the highestvaluefor xin a crosssection ofcountries.Then, a necessaryand
sufficientcondition forbusinesscyclesto
be
lessvolatileand
more
synchronized withtheworld cycle in rich countries isthat
A+Bx*<0.
Thiscondition isalwayssatisfied ifbothtypesof
shocks
generate industry responseswith the rightbiases, i.e.17
Notethat
V
=^(1c)^
+a£
_{n} +_{Sn)}2+(14>K?
+4>(Si +Sl)2
and
a«>n"ten +Sn> +*
m
_{i($iHJi)}C
= Sinceneithery(oo>ft
+**»?)((1oK
+o(U
+S
n
)2
+(14>K
2+<MSi
+^i)2
)
2 2
^,,+^nnor %,+tndependonx,
V
(C) isdownward (upward)slopingifandonlyif (1o)i,_{n +}(1<t>)• %x isdecreasing(increasing) in x.Thepropositiondescribes thesignof
—
1(1o)•Z,_{n +}(1<>)•£,
x Ifor
3xv '
differentparametervalues.
£r
>
Enand
Kn>
k„
. Butthis is nota necessarycondition. Forinstance, itmight bethatthe ccindustryis
more
sensitive todomestic productivity(interestrate)shocks
and
lesssensitive to foreign productivity (interestrate)shocks6—1
6—1
than the (3industry, £r
<
e_{a} (kr< K
a ), yetstill business cycles are6
+
A, 6+
A.less volatile
and
more
synchronized with theworld cycle in rich countries. Thisnaturallyrequiresthatthe ccindustry
be
less sensitive todomesticinterestrate (productivity)shocksand
more
sensitive toforeign interestrate (productivity)shocks,61
,61
,K
P
>K
a—
(ep>e
a
—
).4.
Trade
Integration
The
postwarperiod hasseen
large reductionsin both physicaland
policybarriers to
commodity
trade.Here
we
do
notattemptto explain thesechanges
but instead explorehow
parametric reductions in transport costsaffectthe crosssectionofbusiness cycles. Throughout,
we
assume
that transportcostsare smallenough
relativeto crosscountry differences in factor
endowments
that all countries areeithernetimporters or netexporters ofthe pproduct, for
any
value oftheirdomesticproductivity
and
interest rates,and
forall possible equilibrium prices. Moreover,we
assume
thattransportcosts are smallenough
relative tocrosscountry differences intechnologyin the aindustrythateveryaproduct continuesto
be
produced
in onlyone
country.These
assumptions ensure thatthe pattern oftrade isunchanged
bytheintroduction oftransport costs, although the
volume
oftrade is negatively relatedtothe size of transportcosts.
Remember
thatthemain
theme
of thispaper
is thatthe nature ofbusinesscycles
a
country experiencesdepends on
its industrial structure.As
transport costsdecline, the pricesofproducts inwhich a countryhas comparative
advantage
increaseand, as a result,the share in productionofthese industries increases.
A
naturalconclusion ofthis
argument
is thatone
should expectthatreductionsintransportcosts (globalization?) increase the crosscountryvariation inthe properties
ofbusiness cycles.
We
confirm this intuition here.The
Model
with
Transport
Costs
We
generalize themodel
withmoney
byassuming
thattrade incurs transportcostsofthe "iceberg"variety, i.e. ift>1 units ofoutput are shipped across borders,
only
one
unitarrives at the destinationwhilex1 units "melt" in transit. Let p«(z)and
Pp(z)
now
denote thef.o.b. or international price of variety zofthe aproductsand
ofthe pproducts, respectively.
We
use thesame
normalization ruleas
before in terms of theseinternational prices,and
define p as astheaverage
f.o.b. price ofaproductsrelative to pproducts.
The
presenceof transportcosts implies thatthe c.i.f. ordomestic product prices varyacrosscountries. In
each
country, the c.i.f. prices ofimports
and
importcompeting products are higher than thef.o.b. priceswhile thec.i.f. prices ofexports are equal tothef.o.b. prices. Since countries importall the
varieties ofaproducts they
do
not produce, the c.i.f. price ofall but the infinitesimalmeasure
u.ofdomesticallyproduced aproducts is x _{p}a(z). Similarly, thec.i.f. price ofPproducts is xpp(z) ifthe country is
a
net importerof pproducts,and
_{p}_{p}(z)otherwise.
Note thatthe
consumer
continuesto allocateconsumption
expenditures(evaluated atc.i.f. prices) overcommodities exactlyasbefore.
The
consumer'slaboursupply decision is also
unchanged:
consumers work
ifand
only iftheapplicable
wage,
expressed in termsof a unitofconsumption,exceeds
theirreservation
wage. However,
sinceconsumers
located in differentcountriesfacedifferentc.i.f. prices, theprice of a unitof
consumption
now
variesacross countries.Let_{p}_{c}(n,8,rc,i) denotethe ideal price indexof
consumption
ina
(u.,8,7r,i)country. Thisindexisgiven byxifthe countryis a net importerofthe pproduct,
and
xvotherwise.18 Therefore,we
need
to replace Equations (3)(4) bythefollowinggeneralizations:r s
=
5( r ^YPc
(w
> u=
(18)?UPcy
(24) X (25) 18Toseethis,usethenormalizationruleandrecallthatallcountriesimportallbut theinfinitesmal
numberofaproductsproduceddomestically,andsoincurrthetransportcoston(almost)theirentire
consumptionofaproducts,whichconstituteafractionvoftotalexpenditure. Inaddition,consumersin
countries thatarenetimportersofpproductsfaceac.i.f.priceofxp
pfor theirremaining expenditureon
Pproducts.
Since aproductsare 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 pproducts. In countries thatimport pproducts, the producer price oftheseproducts isTp_{p}, and,
as
a result, Equation (16) hastobe
replaced by: Tp p
=we"
E P7C+KPl (26)Straightforward but
somewhat
tedious algebra revealsthatthe expressionsfor equilibrium pricesin Equations (8), (17)
and
(18) still hold, provided thatwe
replace 8
and
18with 8•x~x
and
x•_{(1}
_{8)} _{if}thecountry _{is} a net importer_{of }pproducts,
and
with 5t4v
and
(18)t~*"v otherwise.19Whiletrade patternsare unchanged, the world
economy
with transport costsexhibits lesscrosscountryvariation in industrialstructures than the world
economy
with free trade.
The
higher the transport costs are, the loweristhe price ofthoseindustries inwhich thecountry has comparative advantage. Thatis, the loweris the price of aproducts (Pproducts) in rich (poor) countries. Forthe reasons
mentioned
before,this leads to
an
reduction inthe share oftheccindustry (Pindustry) in rich(poor) countries.20
19
ToderivetheanalogtoEquation(17),
we
can equatethe ratioofworldexpenditureonthe(sumofall)aproductsinany twocountriestothe ratioof the valueofproductionsasbefore. Usingthenew
expressionsforwagesintheexpressionsforfactorsuppliesresultsin
1 (..,<! A.
Wi
1+x .. / „M x Pa' =Pa
u'6 _{p}C
H6p
_{c}
, Q+X^•
e_{a(*}n,)77r
Ka(ii')•eH+K 1 A . Insertingthisintheideal priceindex
forthe aindustryyieldsthe appropriatemodificationofEquation (17). Equation(8) issimplya
consequenceofourunchangednormalizationrule.ToobtaintheanalogtoEquation (18),notefirstthat thepresenceoftransportcostsimplies thatthemarketclearingconditionsintheaandplndustries
cannowbe expressed asequating the valueofworld productionatproducerprices tothevalueofworld
consumptionatconsumerpricesforallaandpproducts.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 ofincome
isstill given by Equations (11)(12)and
(19)(21). Consequently, Proposition 3 relatingthe properties of businesscyclestoa country'sindustrial structure still holds.
However,
transportcosts reducethevolume
oftrade and, as a result, the crosssectional dispersion inx.This implies thatthecrosssection of businesscycles exhibits less variation in the
model
with transportcoststhan in the freetrademodel.
A
processof parametric reductionsintransportcostshas
opposite effectson
the business cyclesof rich
and
poorcountries. Ifthecompetitionand
cyclical biasesare important,
we
know
thatthe Volatilityand
Comovement
graphs aredownward
and
upward
slopingwith x, respectively. Therefore, reductions intransport costslowerthe volatilityofbusinesscycles in rich countries (as theirx increases)
and
raisevolatility in poorcountries (astheirx decreases). Similarly, reductions intransport
costs
make
business cyclesmore
synchronized with theworld cycle in rich countries(astheirx increases)
and
less synchronized with theworld cycle inpoorcountries(astheirxdecreases).