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Science Research Network PaperCollection at http://papers.ssrn.com/paper.taf7abstract id-=1
OCTl 6 2001
PaperCollection at http://papers.ssrn.com/paper.taf7abstract id-=1
Abstract: Business cycles are both less volatile
world cycle in rich countriesthan in poor ones.
based onthe ideathat comparative
advantage causesrich countriesto specialize in industries that
newtechnologies operated by skilledworkers, while poorcountries specialize in industries that
usetraditional technologiesoperated by unskilled workers. Since
newtechnologies are difficultto imitate, the industries of rich
demandsthan those of poorcountries. Since skilled workers are less likelyto exit
economicconditions, industries in rich countriesface
inelastic labour suppliesthan thoseof poor countries.
asymmetryin industry characteristics
cangenerate cross-country differences in
business cyclesthat resemble those
weobserve inthe data.
Wearegrateful toDaronAcemogluandFabrizio Perriforusefulcomments.Theviews expressed here
Business cyclesare notthe
is thatfluctuations in per capita
incomegrowth are smallerin rich countries than in
poorones, in the top panelof Figure 1,
weplotthe standarddeviation of per capita
incomegrowth against the level of (log) percapita
incomefor a large
Wereferto this relationship asthevolatility graph
andnotethat it slopes
seconddifference isthat fluctuations in per capita
moresynchronizedwith the world cycle in rich countries than in poor ones. Inthe bottom panel of Figure 1,
weplotthecorrelation of percapita
with world average percapita
incomegrowth, excluding thecountry in question,
against the level of (log) percapita
this relationship as the
andnotethatit slopes upwards. Table 1
which is self-explanatory,
showsthatthese facts applywithin different
Whyare businesscycles less volatile
moresynchronized with theworld cycle in rich countriesthan in poor
answer must bethat poor countries exhibit
andpolicy instability, they are less
havea highershare oftheir
economydevoted tothe production of agricultural products
andtheextraction of minerals. Table 1
showsthat, ina statistical sense, thesefactors explain a substantial fraction of thevariation in thevolatility of
muchofthe variation in the
Moreimportantfor our purposes, the strong relationship
andthe propertiesof business cycles reported in Table 1 is still present after
wecontrolfor these variables. In short, there
must beotherfactors behind the strong patterns depicted in Figure 1
differences in political instability,
andtheimportance of natural resources.
Withthe exceptionthatthecomovementgraphseemsto bedriven bydifferencesbetween rich and
poorcountriesandnot within eachgroup.AcemogluandZilibotti (1997)alsopresent thevolatilitygraph.
In this paper,
wedevelop two alternative but non-competing explanationsfor
whybusinesscycles are less volatile
moresynchronizedwith the world in rich
countriesthan in poor ones. Both explanations rely
onthe idea that comparative
causesrichcountries to specialize in industries that require
technologies operated by skilledworkers, while poorcountries specialize in industries that requiretraditional technologies operated by unskilled workers. This pattern of specialization
opens upthe possibilitythat cross-country differences in business
cycles are the result of
betweenthese typesof industries. In particular,
both ofthe explanations
advancedhere predict that industries that
technologies operated by unskilled workers will
moresensitive to country-specific shocks. Ceteris paribus, these industrieswill not only
morevolatile but alsoless synchronizedwith the world cycle since the relative importanceof global shocks is
Tothe extentthatthe business cyclesof countries reflectthose of their
industries, differences in industrial structurecould potentially explain the patterns in
based onthe ideathatfirms using
demandsthan those using traditional technologies.
Newtechnologiesare difficultto imitate quickly
becauseof legal patents. This difficulty confersa cost
advantage ontechnological leaders that shelters
themfrom potential entrants
monopoly powerinworld markets. Traditionaltechnologies are easierto
beencircumvented. This impliesthat
incumbentfirms face tough competition from potential entrants
andenjoy little or
howindustries react to shocks.
Consider, for instance, theeffects of country-specific
production in all industries. In industries that
monopoly power andface inelastic
demandsfor their products.
abroad andtherefore face elastic
demandsfor their products.
result, fluctuations in supply
Tothe extentthat this
competition is important,
incomesof industries that
newtechnologies are likelyto
belesssensitive to country-specific
shocksthan those of industries thatuse
Another explanation for
whyindustries react differentlyto shocks is
the idea that the supplyof unskilledworkers is
moreelastic than the supplyof skilled
Afirstreason for this
asymmetryis that non-market activities are relatively
moreattractive tounskilled workers
wageis lowerthan thatof skilled
abandonthe labourforce, but are notlikelyto affect theparticipation of skilled
asymmetryin labour supply across skill categories
is the imposition ofa
unemployment,butare not likelyto affectthe
employmentof skilled workers.
Thewage-elasticityofthe labour supply also
industries react toshocks. Consider again the effects of country-specific shocksthat
encourageproduction in all industries
andtherefore raisethe labour
demand.Since the supply of unskilledworkers is elastic,these shocks lead to large fluctuations in
employmentof unskilledworkers. In industries that
usethem,fluctuations in supply are therefore magnified by increases in
volatile. Sincethe supply of skilledworkers is inelastic, the
employmentof skilledworkers. In industries that
usethem, fluctuations in supply are not magnified
incomeis less volatile.
asymmetryin the elasticityof laboursupply is important,
industries that use unskilled workersare likelyto
moresensitive to country-specific
shocksthan those of industries that use skilledworkers
weconstructa stylized world equilibrium
modelof the cross-section of business cycles. Inspired bythe
onea world in which differences in both factor
andindustrytechnologies a la Ricardo
combinetodetermine a country's comparative
advantageand, therefore, the patterns of specialization
Togenerate business cycles,
economyto the sort of productivity fluctuations that
wecharacterize the cross-section of business cycles
asymmetriesin the elasticityof product
demandand/or labour supply
usedto explain the evidence in Figure 1. Using available
microeconomicestimatesof the key
andfind that: (i)
modelexhibits slightly less than two-thirds
andone-third ofthe observed cross-country variation in volatility
asymmetryin the elasticityof product
havea quantitatively stronger effect
ontheslopes of the volatility
comovementgraphs, than the elasticity in the labour supply.
Weexplore these results further in sections three
andfour. In section three,
modelto allow for
havereal effectssince firms facecash-in-advance constraints.
howcross-country variation in
developmentaffectthe cross-section of business cycles.
Oncethesefactorsare considered, the calibrated versionof the
modelexhibits roughly the
samecross-countryvariation in volatility
percent of thevariation in
comovementasthedata. In sectionfour,
showthat the two industry
emphasizedhere lead toquite different implications forthe
cyclical behaviorof the termsof trade.
When weconfront these implicationswiththe
data, thepicture that
andconfirms our earliercalibration result.
asymmetryin the labour-supplyelasticity.
Ourresearch isrelatedtothelarge literature onopen-economyrealbusinesscyclemodelsthat
studieshowproductivityshocks are transmittedacrosscountries.See Baxter (1995)and Backus,
Kehoeand Kydland (1995)fortwo alternativesurveysof thisresearch.
two respects. Instead ofemphasizingtheaspects inwhich businesscycles aresimilaracrosscountries,
themeof this paperis thatthe properties of business cycles differ
determinantsof theindustrial structure of a country.
suchdeterminants, that is, a country's ability totrade. In section
betweeninternationaltrade, industrial structure
andthe nature of businesscycles.
Weintroducetrade frictions in theform of "iceberg"transport costs
(modeledhere as parametric reductions in transport costs)
changesthe nature of thebusiness cycles that
countries experience. Iftransport costs are high enough, all countries
andthe cross-section of business cycles is flat.
decline, the prices of products in which a countryhas comparative
doestheir share in production.
Asa result, industrial structures diverge.
Oneshouldtherefore expect globalization to lead to business cyclesthat are
wepresent a stylized
andalsotend to specialize in industries that use these factors intensively. Thatis, the
incomeof a country also determine its industrial
Ourobjective isto develop a formal
frameworkthat allowsus to thinkabout
howcross-countryvariation in industrial structure,
andtherefore income, translates
intocross-country variation in the propertiesof the business cycle.
Weconsidera worldwith a continuum ofcountries with
continuumsof intermediates indexed by ze[0,1],which
werefertoas the a-
andtwo factorsof production, skilled
Thereis freetrade in intermediates, but
donot allowtrade inthe final good.
wealso rule out investment. Jointly, these assumptions imply that countries
Countries differ in theirtechnologies, their
andtheir level of productivity. In particular,
eachcountry is defined
by atriplet (n,5,7t),
advancedthetechnology ofthe country is, 5is the fraction ofthe population that isskilled,
anindex of productivity.
assumethatworkers cannot migrate
differences in technology arestable, sothat \i
and5are constant. Let F((i,5)
Wegenerate businesscycles byallowing the productivity index
nto fluctuate randomly.
Eachcountryis populated by a
level of skills
andtheir personal opportunity cost of work, or reservation
think ofthis reservation
wageas thevalueof non-market activities.
assumethatthis index is distributed accordingto this
Pareto distribution: F(i)
=1-i_x, with X>0.
consumerwith index i
following expected utility:
anywell-behaved utilityfunction; c(i) is consumption of thefinal
anindicatorfunction thattakes value 1 if the
otherwise. Let r(|i,5,7i)
andunskilled workers in a
(H,5,7t)-country. Alsodefine pF(n,8,7t) astheprice of the final good.
constraint is simply pF •c(i)=
w•l(i) for unskilledworkers
andpF •c(i)= r•l(i) for
andonly ifthe applicable real
wageof i" 1
andunskilled workersthat are employed.
Undertheassumption that the
distribution of skills
(2) (3) f - \
<pF if r
>p F if
anytype of workeris less than one, theaggregate labour supplyof this type exhibits awage-elasticityof X. This elasticity
onthe dispersion of reservation
anytype ofworker reachesone,
theentire labour forceof this typeis
employed andthe aggregate laboursupply for thistypeof workers
weconsider equilibria in which the
wagefor skilled workers
>1 , whilethe real
workers is less than one,
—<1 . That is, all countries operate in thevertical region
of their supplyof skilledworkers
andthe elastic region of theirsupplyof unskilled
workers. This assumption generates
asymmetryinthe wage-elasticity of the aggregate laboursupply across skill categories. Thiselasticityis zero for skilled
manycompetitivefirms in thefinal
Thisisthecaseinequilibriumifskilled(unskilled)workersaresufficientlyscarce (abundant) inall
(4) B(pa(z),p p(z))
=V 1-v "1 M) "1 1-e
JpP(z) 1- e dz _0 .0
betweenindustries is one, while theelasticityof
between any twovarieties within
anindustry is9, with 6>1
someworkersthat participatein the labourforce, the
demandforthefinal product is always strong
enoughto generate positive production
Our assumptions ontechnology implythatfirms in the final
spenda fraction vof their
anda fraction 1-v
(3-products. Moreover, the ratioof spending
anytwo a-products z
andz' is given by
andthe ratioof spending
anytwo (3-products z
andp (z) denote theprice of varietyz of the a-
respectively. Define Pn
p asthe ideal price
indices forthe a-
Jpa(z) 1- 9 -dz
and PR =
Jpp(z) 1- e -dz 1 1-e
goodssector are competitive, they set price equals cost. This implies that:
Sinceall intermediates aretraded
oneprice applies, the price
Animplication of this isthat the
goodis nottraded is not binding.
Eachcountry also containstwo intermediate industries.
Thea-industry uses sophisticated production processes that require skilled workers.
Eachvariety requires a differenttechnology that is
variety ofa-products, thefirm that
ownsthe technology requires
e"units of skilled
Asmentioned, the productivityindexn fluctuates
andis not under thecontrol ofthefirms. Let n
measureof a-productsin which thetechnology
ownedby a domestic firm.
nas a natural indicator of
advancedthe technologyof a country is. Itfollowsfrom our
andmarket structurein thefinal
anyvarietyof a-product is 0.
Asa result, allfirms in the a-industry face
and behavemonopolistically. Their optimal pricing policyis to set a
markupover unitcost. Let pjz) bethe price ofthevariety z of the a-industry.
Symmetryensures all thefirmslocated in a (|i,8,7i)-country setthe
pricefor theirvarieties of a-products, p
(7) paa =
markup depends onthe elasticityof
demandfor their products.
The(3-industryuses traditional technologiesthat are available to all firms in all
and can beoperated by both skilled
unit of any varietyof (3-products firms require e" units of labourof
assumedthat inequilibrium skilled
unskilled workers produce (3-products. Sinceall firms in the (3-industry
have accessto the
sametechnologies, they all faceflat individual
Theyset priceequal to cost. Letp (z)
bethe price ofthevariety z of
Symmetryensures that all firms in the P-industryof a (n,5,7r.)-country
sameprice forall varieties of (3-products, p^n,S,n):
(8) pp =w-.e-"
With this formulation,
asymmetryin the price-elasticity of product
demand.This elasticity is in the a-industry
andinfinity inthe (3-industry.
Business cycles arise as
sumof a global
onthe interval [-1,1] with
instantaneous variance equalto r\a2
and(1-r|)rj2 respectively, with
a>0. Letthe initial distribution of country-specific
assumethis distribution is independentof other country
changesin these country-specific
componentsare independent across countries,
distribution of 71-n istime invariant.4
Werefer tothisdistribution as G(7i-n). While
anindex of domesticproductivity,
aregulates thevolatilityofthedomestic shocks.
betweendomestic shocks, dn,
andforeign shocks, dn,
is therefore Jr) .
parameterti therefore regulates the extentto which the
variation in domestic productivity is
dueto global or country-specific
dnor d(7i-n). Figure 2
nareattheir respectiveboundaries.These arerareevents since
Acompetitive equilibrium ofthe world
Our assumptionsensurethat a competitive equilibrium exists
Weprovethis byconstructing theset of equilibrium prices.
In thea-industry, different products
(sumof all) a-products of a (^,5,7i)-country
mustequal the ratio of supplies is
condition plus Equation (2)
andthe definition of P
wefind that: . Usingthis (9) Pa
H1 ^9 n-n
Since the distribution functions F(u.,8)
andG(n-n) aretime-invariant, x
¥a is aconstant. Since
eachcountry isa "large" producer of its
ownvarieties of a-products, the price ofthesevarieties
onthe quantityproduced. Countrieswith
manyskilled workers (high 8)
with relatively high productivity (high 7i-n) producing a small
numberof varieties (low
|i) produce large quantitiesof
eachvariety ofthe a-products
andas a result, face low prices.
As9^>°°, the dispersion in theirprices disappears
Inthe (5-industryall products
sameprice. Otherwise, low-price
varieties of (3-products would not
beproduced. Butthis is nota possible equilibrium given the technology described in Equation (4). Therefore, itfollows that:
computethe relativeprice of both industries.
the ratio of world spending in the a-
and(3-industries, ,to the ratio of thevalue
of their productions,
^. Using Equations (2)-(3)
then find that:
P1 f v
—n 1+Xv •e*
andis constant. IfX>0, high productivity is
associated with high relative pricesfor a-products as theworld supplyof (3-products
is high relativeto thatof a-products. This increasein the relative supplyof (3-products
dueto increases in
AsA.-^0, the relative prices of
both industries are unaffected bythelevel of productivity.
Whatare the patterns oftrade inthisworld
andtheshare of the a-industry in a (n,5,7i)-country, i.e.
/ \ d •s•o
—. Notsurprisingly, countrieswith better
technologies (high n)
humancapital (high 5)
havehighvalues for both y
Wetherefore refer to countries with high values ofx
asrich countries. Since
numberof varieties of a-products
themin the production offinal goods, all countries exportalmost all of their
production of a-products
andimportalmost all of the a-products
usedin thedomestic production of final goods.
ashareof income, these exports
andimports are x
Tobalancetheir trade, countrieswith
andx-v, respectively. Therefore, the share of trade in
Asusual, thistrade can
decomposedinto intraindustry trade, min[v,x],
Theformer consistsof trade in productsthat
Thelaterconsistsof trade in productswith different factor
modelthereforecaptures in a stylized
mannerthree broad empirical regularities regarding the patterns of trade: (a) a large
volumeof intraindustry trade
amongrich countries, (b) substantial interindustrytrade
economydescribed in the previoussection, countries are subject
sametype of country-specific
in the properties oftheir business cycles
must beultimately attributed to differences
andfactorproportions. This is clearly asimplification. Inthe real
world countriesexperience differenttypesof
andalso differ in
andfactor proportions. With thiscaveat in mind, in this section
muchof the observed cross-countryvariation in business cycles could potentially
modelof theprevious section?
andtwo thirds ofall the variation.
Thefirst steptowards answering this question isto obtain
incomegrowth tothe shocksthat countries experience. Applying Ito's
the definition of y
andusing Equations (2)-(11),
alinearcombination of country-specific
global shocks: (12)
Equation (12) provides a complete characterization ofthe businesscycles experienced by a (u.,5,7i)-countryas afunction ofthe country's industrial structure,
measuredbyx. Equation (12)
showsthat poorcountries are
country-specific shocks, i.e.
is decreasing in x. Equation (12) also dn=o
showsthatall countries are equally sensitive to global shocks, i.e
Wenextdiscuss the intuition behind these results.
a-and(3-industryface both perfectly inelasticfactor
onepercent country-specific increase in productivity
employmentor product prices.
and incomealso increase by
onepercent. This is
=1 if A.-^0
6^^.If A,is positive, a country-specific increase in
employmentof A. percent in the
(3-industryand, as a result, production
and incomeincrease by
employmentresponse magnifiesthe expansionary effects of increased
productivity in the (3-industry.
Asa result, the
hasstronger effects in poor 3dlny
8—>°°. If6 is finite, a country-specific dn=o
increase in productivity of
onepercent leads toa 0"1
decreasein prices inthe
responsecounteracts the expansionaryeffects of increased productivity inthea-industry. Consequently, the
weakereffects in rich
Bdlny countries, i.e.
X>0 and9 isfinite,
havethat both the
makepoor countries react
country-specific shocks, i.e.
+X) is decreasing in x.
Whyareall countries equally responsiveto global
shocks?This result rests
ontheassumption thattheelasticity of substitution
one. Consider a global increase in productivity.
onehand, production of p-products
expandsrelativeto the production of a-productsas
moreunskilled workers are employed. Ceteris paribus, this
wouldincrease the share ofworld
and hencepoorcountries, aftera positive global shock. But theincrease in relative supply lowers the relative price of p-products. This reduces theshare ofworld
goesto the P-industry,
and hencepoorcountries, after a positive global shock.
production ofthe final
goodimplies that thesetwoeffectscancel
world spending in the a-
andP-industries remains constant overthe cycle. Therefore,
frameworkdifferences in industrial structure
donotgenerate differences in
countries react to global shocks.6
modelto interpretthe evidence in Figure 1. Define
astheworld average growth rate, i.e.
dFdG. Then, it follows
from Equation (12) that:
Sincethe lawof large
numberseliminates the country-specific
shocksin the aggregate, the world
anyofthe countriesthat belong to it.
WhiletheCobb-Douglasformulation isspecial, itisnotdifficulttograsp whatwould happenifwe
relaxed it. Iftheelasticity ofsubstitutionbetween industrieswerehigherthan one, poorcountrieswould
be moresensitivetoglobalshocksthanrichcountriesastheshareofworld incomethatgoestothe
|3-industry increasesafterapositiveglobalshock and decreasesafteranegative one. Iftheelasticity of substitutionwere lessthan one, the oppositewould betrue.
Once again,this resultrestsontheCobb-Douglas assumption. Iftheelasticityofsubstitutionbetween
a-and|3-productswere higherthan one, the very richcountries mightexhibitbusinesscyclesthatare
denotethe standarddeviation of
incomegrowth of a
denotethecorrelation of its
incomegrowth with world
Theseare the theoretical analogs to thevolatility
graphsin Figure 1. Using Equations (12)-(13)
+X) -i2 (1"T1)+ '
Figure 3 plotsthe volatility
graphsasfunctionsof x, for
differentparameter values. Exceptin the limiting
Theintuition is clear:
Asa result of
asymmetriesin theelasticity of
andlabour supply, the a-industryis less sensitive to country-specific
makesthe a-industry lessvolatile
world cyclethan the (3-industry. Sincecountries inherit the cyclical properties of their
incomesof rich countries are also lessvolatile
moresynchronized with the world cyclethan thoseof poorcountries.
magnitudeof these differences
Xincreases and/or 6 decreases.
Asimple inspection of Equations (14)
and(15) revealsthat there existvarious combinations of
parameterscapable of generating approximatelythe data patterns displayed in Figure 1
andTable 1. Inthis sense, the
modelis able to replicate the
evidencethat motivated the paper. Butthis is a very
byrestrictingthe analysis tocombinations of parameter values that
choosevaluesfor a, r\, v
businesscycles varies with X
and9. Needlessto say,
strong conclusionsfrom a calibration exercise likethis in a
Asnoted above, in the realworld countries experience differenttypesof
availableestimates of the key parameters
andindustries, sothat caution is in order
whengeneralizing to the largecross-section of countries
westudy here. Despite these caveats,
someuseful insights can
begained fromthis exercise.
Todeterminethe relevant rangeof variationforx,
modelpredicts thatthe share of exports in
incomein rich countries is x.
Sincethis share is
around 60percent inthe richest countries in our sample,
0.6 as a reasonable upper
modelalso predicts that v is theshare of exports in
incomein poor countries,
andthat in these countries x<v. Sincethe share
of exports in
around 20percent inthe poorestcountries in oursample,
anduse0.1 as alower
problematic, since there are
noreliableestimates of the volatility
andcross-country correlation of productivitygrowth for this large cross-section of countries.
a andr| to
matchtheobserved level of volatility
incomegrowthforthetypical rich country, given the rest of our parameters.8 This
meansthatthis calibration exercise
canonly tell us aboutthe
match observedcross-country differences involatility
Thetop-left panel ofTable 2 reportsthe resultsof this calibration exercise,
shownin Figure 3.
Thefirst row reportsthe predicted difference in volatility
betweenthe richest country(with log per capita
GDPof around 9.5)
andthe poorestcountry (with log percapita
GDPof around 6.5),
based onthe regressionswith controls in Table 1.
In particular,a andr|arechosentoensurethatV=0.04 andC=0.4,forx=0.5,v=0.2andthe given
report the difference involatility
betweenthe richest (x=0.6)
poorest (x=0.1) countries thatthe
modelpredicts fordifferent valuesof
microeconomicestimates. Available industry estimates ofthe elasticity of export
demandrange from 2to 10 (see Trefler
andLai (1999), Feenstra, (1994)), whileavailable estimatesforthe labour supply elasticity of
unskilled workers range from 0.3 to 0.35
Murphy andTopel (1991)).
Thetable also reports thevaluesfor
andr\that resultfrom the calibration procedure.
showsthat, using values for8
9=2 andA.=0.35, the
can accountfor nearlytwo-thirds ofthe cross-country difference in volatility
andpoorcountries (-0.016versus -0.026),
andslightly lessthan one-third ofthe cross-country differences in
comovement(0.129 versus 0.382).
Thesevalues forthe parameters are within the range
be evenstronger, say 9=1.2
andX=0.7, the predicted differences in volatility
comovementare closerto their predicted values.
twohypotheses put forward here
accountfora sizeable fraction of cross-country differences in business cycles
model asours. Moreover,
seein the next section that a simple extension ofthe
andcross-country differences in the
movethetheoretical predictions closerto the data.
secondresultin Table 2 isthatthe
asymmetryin theelasticity of product
asymmetryin theelasticity of
the labour supply. Within the range of
parametervalues considered in Table2,
onthe slopeof the two graphs, while
Tothe extentthatthis range of parameter values
consider is the relevant one, this calibration exercise suggeststhat the
asymmetriesin the elasticity of product
whybusiness cycles are different across countries.
Wereturn to this
point in section four
between hypotheses by
Oursimple calibration exercise tells us thatthe two industry
account for almosttwo-thirds of the cross-country differences in volatility,
andnearly one-third ofthe cross-country variation in
Onereaction tothisfinding is
modelis surelytoo stylized to
beconfronted with the data. Afterall,
mostof our modelling choices
maximizetheoretical transparency ratherthan
themdeveloped, it is timeto build
reality by adding details. This is the goal of this section,
helps to significantlynarrowthe
between model anddata. This is not the only
wayto narrow this gap, but
chooseto followthis route
this extension highlights areboth realistic
andinteresting in their
nowallow countriesto differalso in theirdegree offinancial
Eachcountry is therefore defined by a quintuplet,
wherek is a
degreeof financial development,
andi isthe interest rate
assumethatk is constant over time
re-define F(^,5,k) asthe time-invariantjointdistribution of \i, 8
additional source of business cyclesby letting ifluctuate randomly.
Wemotivate the use of
assumingthatfirms facea cash-in-advance constraint.9 In particular, firms
use cashor domestic currency in orderto
afraction k of their
wagebill before production starts, with
howunderdeveloped are credit markets.
k^Oin all countries,
wereach the limit inwhich credit marketsare so efficientthat
SeeChristiano,Eichenbaum andEvans (1997)fora discussionof relatedmodels.
This is the
havestudied so far. In thosecountries
wherek>0, firms borrow
cashplus interest after production is
andoutput is sold to
Monetarypolicy consists of settingthe interest rate
distributing the proceeds in a
in the literature
random.10 In particular,
assumethatthe interest rate is a reflecting Brownian motion
onthe interval [i,T], with
andare independent acrosscountries
changesin n. Letthe initialdistribution of interest rates
beuniform in [t,T]
the distribution of othercountry characteristics. Hence, the cross-sectional distribution of i, H(i),
moneyleads onlyto minor
changesin thedescription of
world equilibrium in section one. Equations (2)-(3) describing the labour-supply
andthe numeraire rule in Equation (5) still apply. Sincefirms in thefinal
wages,their pricingdecision is still given by Equation (6).
cash-in-advance constraintsaffect thefirms in the a-
face financing costs in addition to labour costs.
Asa result, the pricing equations (7)-(8)
Thissimplification isadequate ifonetakes the viewthatmonetarypolicy hasobjectivesotherthan
stabilizingthecycle. Forinstance,iftheinflationtaxisusedtofinancea publicgood, shockstothe
marginal valueof thispublicgoodare translatedintoshockstotherateofmoneygrowth. Alternatively,if
acountryiscommittedtomaintainingafixed parity,shockstoforeign investors'confidence inthe
country aretranslatedintoshockstothe nominalinterestrate, asthe monetaryauthoritiesusethe latter
changesin theinterest rate affectthe financing costs of firms
are therefore formally equivalenttosupplyshocks such as
changesin production or payroll taxes. Formally, this isthe only
showsthat Equations(9)-(11) describing the set of equilibrium
prices arestill valid provided
which converges to the earlier definition of
B inthe limiting
in which k-^0 in all
Financing costs are not a directcost forthe country
wholebut only a transferfrom firms to
consumersvia the government. Consequently,
/ \ p -s-e"
shareof the a-industry are still defined
Nowrich countries arethosethat
havebettertechnologies (high n),
humancapital (high 5)
ceterisparibus, a highvalue for u.
andS lead to a high valueof x. This is
beenreferring tocountries with high values for xas rich.
nowthat a low valuefor k leads to both higher
income anda lower value for x.
Ahigh valueof k is associatedwith higher financing costs
demandforall typesof workers. Inthe market for skilledworkers, this
demandis translated fully into low in
noeffects in employment.
Thesize of the a-industry istherefore notaffected by cash-in-advance constraints. In
the marketfor unskilled workers,this
demandis translated into both lower
Thelatter implies a smaller (3-industry. Despite this,
continueto referto countries with highervalues ofxas rich. That is, it
moreimportant determinantsofa country's industrial structurethan the
Weare readyto determine
the cross-section of businesscycles. Applying Ito's
find this expression forthe
(demeaned)growth rate of
incomeforthe (|n,5,7t,K,i)-country: (18) dlny-E[dlny]= x
Equation (18), which generalizes Equation (12), describes the business cycles of a (|j,,S,7i,K,i)-country
afunction of its industrial structure.
describe the reaction of thecountryto productivity
beendiscussed at length.
Thethird term is
howthe country reactsto interest-rate shocks. In particular, it
and havea low
degreeoffinancial development. That is,
is decreasing in x
andincreasing in k (holding constantx). d(rc-n)=o
Anincrease in the interest rate raisesfinancing costs in the a-
(3-industries. This increase is larger in countries with low
development(high k). Just
becauseofthis, poorcountries are
moresensitive to interest-rate
shocksthan rich countries. But there is more. Inthe a-industry,the supply of labour is inelastic
andthe additional financing costs are fully
workers in theform of lower
wages.Production is therefore notaffected. Inthe
f3-industry, thesupplyof labour is elastic
andtheadditional financing costs are only
andproduction thereforedecline. In the
and incomedecline after a positive interest-rate shock. But if
asymmetryin the laboursupply elasticity is important, this reaction should
stronger in poorcountries that
havelarger (3-industries. This provides a
moresensitiveto interest-rate shocks than rich
Theintroduction of interest-rate
shocksprovides two additional reasons
through their industrial structure
consequenceof their lack of
financial development. Both of theseconsiderations reinforcethe results of the
Equation (13) still
andthe lawof large
numberseliminatestheir effectsin the aggregate. Then, rewrite the volatility
graphs asfollows: (19)
1+Xf 1 +
x^ \ 1
X-v2 12 Tl
X-v2 ,,-2 I* „\2 t2 •Tl
Theseequations are natural generalizations of Equations (14)-(15).
showthat, ceteris paribus, countrieswith lowfinancial
andless correlated with the world.
which industrial structure affectsthe business cycles ofcountries.
With these additionalforces present, the
come muchclosertothe observed cross-countryvariation involatility
comovementusing values for9
and Xthat are consistentwith available
microeconomicstudies. This is
shownin the bottom panelof Table 2,
assumethatthe standard deviation of
monetarypolicy is 0.1
andthatk=1 in the poorest countries in our
sample andk=0.5 in the richest countries. For
9=2 andX=0.35, the extended
nowdelivers cross-country differences in volatilitythatare nearly identical tothe
weestimated in Table 1 (-0.024versus -0.026),
andcross-country differences in
weobserve in reality(0.165 versus 0.382). Looking further
wecan further improvethe fitof the
this is achievedat the cost of over-predicting cross-country differences in volatility.
Wecould tryto furthernarrowthe
considering additional extensions to the model. But
wethink thatthe results obtained sofar are sufficientto establish that thetwo hypotheses considered here
havethe potential to explain at least in part
whybusiness cycles are different in rich
andpoor countries. This isour simple objective here.
Fromthe standpoint of the evidence reported in Table 1
developed in the previous sections, the two industry
asymmetriesstudied hereare observationally equivalent.
and Xas additional evidence to calibrate the model,
wefound that the
morepromising explanation of
cycles aredifferent across countriesthan the
asymmetryin theelasticity of the labour supply. Inthis section,
implications forthe cyclical properties of theterms of trade,
andthen confronting these implications with thedata.
onthecyclical behavior of theterms of
trade is consistent with the results ofour calibration exercise. Namely, a strong
asymmetryinthe elasticityof product
accurate description of theterms oftrade datathan a strong
elasticityof the labour supply.
Wefirstderivethe stochastic process forthetermsof trade.Let T((i,5,7t,k,i)
termsof trade of a (|a,5,7r,K,i)-country. Using Equations (9)-(11),
thatthe (detrended) growth rate in theterms of trade is equalto:12
Itispossibletodecomposeincomegrowthintothegrowth ratesofproductionandtheterms oftrade.
GDPgrowthrate)measuresincomegrowththat isdueto changesin
production, holding constantprices.Thegrowthrate ofthetermsoftrademeasuresincome growththat
isduetochanges in prices,holdingconstant production.
termsoftradeofa countryasthe ideal priceindexofproductionrelativetotheideal price indexof
expenditure.Thegrowth rateofthetermsoftradeisequaltotheshareofexportsin incometimesthe
Equation (21) describes thecyclical behaviorof thetermsof trade as
function ofthe country's industrial structure. It
showsthat positive country-specific
shocksto productivity affect negativelytheterms of trade,
andthiseffectis larger (in
absolute value) the richer is the country, i.e. is negative
decreasing in x. Equation (21) also
worsenthe termsof trade of poor countries
andimprove thoseof rich countries, i.e. ~\f-iI—
is negative if
andpositive ifx>v. Finally, Equation (21)
ontheterms of trade.
behind these results in turn.
have noeffecton import prices
becausecountries are small. But they
doaffectexport prices. Consider a positive country-specific
shockto productivity. In the a-industry, firms react to the
howto produce. Sincethis set is small, the increase inthe production of
eachvarietyis large. Since domestic
varietiesare imperfect substitutes, the increase in production lowers the price ofthe country's a-products. Inthe P-industry, firms
howto produceall varieties.
shockbyspreading their production
somefirms abroad to
Asa result, the increase in the production of
eachvarietyis infinitesimally small
andtheprices of the country's p-products are not affected. In the aggregate, theterms of trade
worsenas a result of
the shock. But if the
asymmetryin theelasticity of product
demandis important, the termsof trade shoulddeteriorate
morein rich countries.
Global shocks influence all countries equally and, consequently, they
donot affect the prices ofdifferentvarieties of a-
andP-products relativeto their
corresponding industryaggregates. Consider a positive global
shocklowers the price of all (3-products relative to all
Thereason is simple: In both industries, the increase
in productivity leads to a directincrease in production. But if the
elasticity ofthe labour supply is important, the increase in productivity raises
employmentof unskilled workers
andleads to afurther increase in theproduction of
Astheworld supplyof (3-products increases relative to that of a-products,
their relativeprice declines. This is
whytheterms oftrade of net exporters of
|3-products, x<v, deteriorate, while theterms oftrade of net importers of p-products, x>v, improve.
Finally, Equation (21) states that country-specific interest-rate
donot affect import prices
becausethe country issmall. Butthey
donot affect export prices either.
donot affect the production of a-products.
Asa result, they
donot affect theprices ofdomesticvarieties relativeto the industryaggregate. Interest-rate
shocksaffect the production of (3-products.
However,firms in the p-industrycannot
changetheir prices intheface of perfectcompetition from firms abroad.Therefore, country-specific
donotaffect the termsof trade.
cyclical behaviorofthe terms oftrade. Inthe
asymmetriesin the elasticity
ofthe labour supply,
A—>0, only country-specific
asymmetriesin the elasticityof product
demand,8-^°=, only global
shocksaffect theterms of trade. This
comovementgraphs fortheterms of trade. Let
denotethe standard deviation of the(detrended) growth of termsof trade of a (|a,8,7t,K,i)-country,
CJ(\i,5,n) denote its correlation with world
incomegrowth. Using Equations
CT = (1-il)+ V
Tounderstandthe intuition behind theseformulae, it is useful toconsidertwo
extremecases. Both are illustrated in Figure 4, which plots the volatility
comovementgraphsof theterms oftrade asfunctions of x, fordifferent parameter values.
Assumefirstthatthe only reason
whybusiness cycles differacross countries
asymmetryin the elasticityof product
upwardsloping. Sinceall the
volatility in prices is
changesin thedomestic varieties of a-products, the terms of trade are
morevolatile in rich countries
wheretheshare ofthe a-industry is large.
comovementgraph isflat at zero. Whilethe termsof trade respond onlyto country-specific shocks, world
incomeresponds onlyto global shocks.
both variablesare uncorrelated.
Assumenextthat the only reason
whybusiness cycles are differentacross
countries is the
asymmetryin the elasticityofthe labour supply, i.e. 0^><». Then, T lx-v|-X i— T 1-1 if x <v
Thevolatilitygraph looks like
A.v[ 1 if x
whenx=v. Since all the volatility in prices is
aggregate industry prices, theterms oftrade are
morevolatile in countries
wherethe share of interindustrytrade in overall trade is large, i.e. | x-v|is large.