C A H I E R 0 7 - 2 0 0 0
I N T E R N A T I O N A L T R A N S M I S S I O N O F T H E
B U S I N E S S C Y C L E I N A M U L T I - S E C T O R M O D E L
S t e v e A M B L E R ,
E m a n u e l a C A R D I A a n d
C h r i s t i a n Z I M M E R M A N N
Université de Montréal
Centre de recherche
et développement en économique
C.P. 6128, Succursale Centre-ville
Montréal (Québec) H3C 3J7
Téléphone : (514) 343-6557
Télécopieur : (514) 343-5831
Adresse électronique :
crde@crde.umontreal.ca
Université de Montréal
Centre de recherche
et développement en économique
C.P. 6128, Succursale Centre-ville
Montréal (Québec) H3C 3J7
Téléphone : (514) 343-6557
Télécopieur : (514) 343-5831
CAHIER 07-2000
INTERNATIONAL TRANSMISSION OF THE BUSINESS CYCLE
IN A MULTI-SECTOR MODEL
Steve AMBLER
1
, Emanuela CARDIA
2
and Christian ZIMMERMANN
1
1
Centre de recherche sur l'emploi et les fluctuations économiques (CREFÉ),
Université du Québec à Montréal
2
Centre de recherche et développement en économique (C.R.D.E.) and
Département de sciences économiques, Université de Montréal
April 2000
__________________
The authors would like to thank Brian Copeland, Martin Boileau, and participants at the
Canadian Macro Study Group and the Society for Economic Dynamics and Control
meetings for helpful discussions and comments on previous versions of this paper, and
the Fonds pour la Formation de chercheurs et l'aide à la recherche (FCAR) of Québec for
RÉSUMÉ
Les modèles multi-pays n’ont pas réussi à reproduire des aspects importants de la
transmission internationale des cycles économiques. Les modèles standards prédisent
des corrélations inter-pays de l’output et de la consommation qui sont respectivement trop
faibles et trop élevées. Dans cet article, nous construisons un modèle multi-pays de cycle
économique avec des secteurs multiples afin d’analyser le rôle des chocs sectoriels dans
la transmission internationale du cycle économique. Nous trouvons qu’un modèle avec
des secteurs multiples génère une corrélation inter-pays de l’output plus élevée que les
modèles standards à un secteur et une corrélation inter-pays de la consommation plus
faible. De plus, il prédit des corrélations inter-pays de l’emploi et de l’investissement qui
sont plus proches des données que le modèle standard. Nous analysons également les
effets relatifs des secteurs multiples, du commerce des biens intermédiaires, de la
substitution entre les biens domestiques et étrangers, de la préférence locale, des coûts
d’ajustement du capital et de la dépréciation du capital sur la transmission internationale
du cycle économique.
Mots clés : macroéconomie d’économie ouverte, cycles économiques, chocs sectoriels
ABSTRACT
Multi-country models have not been very successful in replicating important features
of the international transmission of business cycles. Standard models predict
cross-country correlations of output and consumption which are respectively too low and too
high. In this paper, we build a multi-country model of the business cycle with multiple
sectors in order to analyze the role of sectoral shocks in the international transmission of
the business cycle. We find that a model with multiple sectors generates a higher
cross-country correlation of output than standard one-sector models, and a lower cross-cross-country
correlation of consumption. In addition, it predicts cross-country correlations of
employment and investment that are closer to the data than the standard model. We also
analyze the relative effects of multiple sectors, trade in intermediate goods, imperfect
substitution between domestic and foreign goods, home preference, capital adjustment
costs, and capital depreciation on the international transmission of the business cycle.
Dynamicgeneralequilibriummodelshavebeenquitesuccessfulin replicatingalargenumberofthestylized
facts of the business cycle. However, multi-countrymodels havedone less well in replicating the stylized
facts oftheinternationaltransmissionof thecycle. Inarecentsurveyarticle, Backus,KehoeandKydland
(1995,henceforthBKK)discusstwomainpuzzlingfeaturesofthedatathatarehardforgeneralequilibrium
modelsto capture. 1
First, there is what BKK refer to as a quantity anomaly. In the data, cross-country correlations of
outputaregenerallyhigherthancross-countrycorrelationsofaggregateproductivity(asmeasuredbySolow
residuals), and the latter are generally higher than cross-countrycorrelations of consumption (see Table
3 below). Inaddition, cross-countrycorrelations of consumption and investment are generallypositive in
the data. In standard models, the ordering of the output, Solow residual and consumption correlations
is reversed. Risk sharing between agents in dierent countries leadsto high cross-countrycorrelations of
aggregate consumption. Incentives to use inputs where they are most productive often lead to negative
cross-countrycorrelationsofoutputandespeciallyofinvestmentandemployment.
Second,there isaprice anomaly. Generalequilibriummodels donotgenerate uctuationsintheterms
oftradeaslargeasthoseobservedin thedata. Modelswhichrestricttheelasticityofsubstitutionbetween
domestic and foreigngoodscan generatevolatileterms of trade, but at the costof acounterfactuallylow
volatilityof uctuationsintradebalances.
This paper is a contribution to the literature on explaining the quantity anomaly. We modify the
supplysideof thestandardmulti-countrybusinesscycle modelby introducing multiple sectorsand traded
intermediateinputs. ThemainmotivationforthischangeisthestudybyLongandPlosser(1983),oneofthe
seminal contributionsto theliteratureonreal business cycle(RBC) models. Theyshowthat uncorrelated 1
SeealsoAmblerandCardia(1995)onthecross-countrycorrelationsofmacroeconomicaggregatesandBaxter(1995)fora broadsurveyofinternationalbusinesscyclemodels.
changesindemandforintermediateinputsproducedbythosesectors. Apositiveinter-sectoraltransmission
of productivity shocks in a closed-economy model could lead to a positive international transmission of
sectoralshocksinamulti-countrymodel.
Wend that the introduction of multiple sectors brings thepredictions ofthe model closer to what is
observedin thedata. Comparingthepredictionsof our multi-sectormodelwith those of astandard
one-sectormodelyieldsthefollowingresults. Themulti-sectormodelpredictsahighercross-countrycorrelation
ofoutputthan theone-sectormodel,andit predictsaslightlylowercross-correlationof consumption. The
multi-sector model alsopredicts cross-countrycorrelations of investmentand employment that are
signi-cantlylessnegativethantheone-sectormodel.
The paper is structured as follows. In the next section, we brie y review the stylized facts of the
international transmission of the business cycle, we survey some recent papers that have attempted to
explain thequantityanomaly, and wedescribehowour model diersfrom othersin the literature. Inthe
thirdsection,wepresentourmodelanddescribehowtocalculateitscompetitiveequilibriumasthesolution
to asuitablesocial planningproblem. Inthefourthsection,wediscussthemodel's steadystateproperties
anditscalibration. Inthefthsection, wepresenttheresultsfromnumericalsimulationsofatwo-country
two-sector version of ourmodel. We consider results for abase-case calibration and report theresults of
sensitivityanalyses. Wepresentourconclusionsin thesixthsection.
2 Stylized Facts and Relevant Literature
2.1 The Facts
Tables2and3containrowswhichillustratethestylizedfactsoftheinternationaltransmissionofthebusiness
Zimmermannusesquarterlydatafrom19industrializedcountriesfrom1960:1to1991:2. Table2dealswith
comovementswithin individualcountries. Asidefromtherealexchangerate(termsoftrade)andthetrade
balance,thesestylizedfactsarewellknownfromtheclosed-economybusinesscycleliterature,andaresimilar
acrossindustrialized countries. Consumption and employment areless volatile thanoutput, investmentis
morevolatile thanoutput, andaggregatesarehighly correlatedwith output,except forthetrade balance.
In thecase of theterms of trade and thetrade balance, theU.S. data are lessrepresentative. Theterms
oftrade aremorevolatilethanGNP forallcountriesin thesample, but thecontemporaneouscorrelations
between the terms of trade and GNP and betweenthe trade balance and GNP vary quite a bit overthe
sample. Figure1showshistogramsforthesetwostatisticsforthecountriesin Zimmermann'ssample.
Table3 reportsstatistics which are moreclosely relatedto theinternationaltransmission ofthe cycle.
Thecross-countrycorrelationsintherstrowofthetablearebetweenU.S.aggregatesandthecorresponding
aggregateinagroupofEuropeancountries. Thecross-countrycorrelationofconsumptionislowerthanthe
cross-countrycorrelationofoutput. Thecross-countrycorrelationof investmentisslightlyhigherthanthe
cross-country correlationof consumption, and thecross-countrycorrelation of employment is signicantly
positive.
Thecross-countryaveragescalculatedbyZimmermann (1995)andreported in thesecondrowofTable
3 supports the quantity anomaly, in spite of the fact that the average cross correlations are lower than
for theU.S. In Figure 2we explorethe data in moredetail byreporting histogramsfor thecross-country
contemporaneouscorrelations of dierent aggregates. The gure shows that the mean values reported in
the second column of Table 3 mask a signicant amount of variation across the countries in the sample.
Theordering implicitin thequantity anomalyis notrespectedfor allcountriesin thesample. Looking at
leadsorlagsofuptofteen quarters,thecrosscorrelationof consumptionishigherthanthatofoutput in
50%of all possible cases. The contemporaneouscross correlations of Solow residualsare higher than the
contemporaneous cross correlations of output in 19%of possible cases, implying a negativeinternational
transmissionoftechnologyshocks. Thedataindicatethatthequantityanomalyisnotasstrongasimplied
bytheU.S.dataalone.
2.2 Recent Literature
Severalrecentstudiesattempttobuildmodelscompatiblewiththesefeaturesofthedata. Someproceedby
modifyingtheconstraintsontradesamongagents. Kollmann(1992),BaxterandCrucini(1995),Heathcote
andPerri(1997)andArvanitisandMikkola(1996)buildmodelswithincompleteassetmarketswhichreduce
the incentive for risk sharing. These authors nd that incompletemarkets help reduce the cross-country
correlation of consumption, but the cross-country correlations of output, investment and hours worked
remain counterfactually negative. Kehoe and Perri(1996) build a model in which international loans are
notperfectlyenforceable,sothatthedegreeofmarketincompletenessisendogenous. Theirmodelgenerates
positivecross-countrycomovementsof output,investmentandemployment. Rickettsand McCurdy(1995)
buildatwo-countrymodelwithmoneyanddieringratesoftrendproductivitygrowthacrosscountries. In
theversionof theirmodelin whichthere isnointernationaltradein investmentgoods, so thatinvestment
goods in a given country must be produced in the same country, they obtain a relative ordering of the
cross-countrycorrelationsthat iscompatiblewiththedata.
Other studies modify the specication of agents' preferences. Devereux, Gregory and Smith (1992)
developamodel withaparticulartypeof nonseparabilitybetweenconsumptionand leisure. Theysucceed
inloweringthecross-countrycorrelationofconsumption. StockmanandTesar(1995)introduceanontraded
investment or hours worked. They also introduce taste shocks that displace preferences between traded
andnontradedgoodsinorderto increasethepredictedvariabilityofboththetermsoftradeandthetrade
balance. The quantity anomaly remains for the traded goods sectors. Finally, Canova and Ubide(1998)
develop atwo-countrymodel with home production. Theirresults indicate that their model cangenerate
cross-countrycorrelationsofoutputsimilartothoseofconsumption,andthatitcangeneratepositive
cross-countrycorrelationsofinvestmentandemployment.
Severalpapersin theliteraturebuild closed-economybusiness cyclemodelswithmultiple sectors. Long
and Plosser (1983) is an early example. They analyze a multi-sector model of a closed economy which
matches the input-output structure of the U.S. economy at a coarse level of disaggregation. They show
that uncorrelated sectoral productivity shockscan leadto positive comovementsin outputacross sectors.
Hornstein and Praschnick (1997) distinguish between an intermediate and a nal goods sector and show
thatsectoralproductivityshockscanleadtopositivecomovementsinoutputacrosssectors. Horvath(1998)
buildsahighlydisaggregatedmulti-sectormodelofaclosedeconomy.
Veryfewpapershaveincludedmultiplesectorsinatwo-countrymodeltoexaminethequantityanomalies
discussed byBKK.Costello andPraschnick(1993)developatwo-countrymodel which disaggregateseach
economyintoonesectorwhichproducesanintermediategoodandasinglenalgoodssector. Thenalgoods
in the twocountries areperfect substitutes. With complete markets and separability betweenleisure and
consumptionintheutilityfunction,consumptionisperfectlycorrelatedacrossthetwocountries.Theirmodel
predictsahighercrosscorrelationofoutputthan theBKKmodel. Thepaperdoesnotexaminethe
cross-countrycorrelations ofinvestment andemployment, which areimportant aspectsof thequantity anomaly
documented in BKK. Head(1997)builds atwo-countrymodel with dierentiated intermediate goods and
aprimarygoodssector(whoseoutputisusedasanintermediateinputinmanufacturing),amanufacturing
sectorwhose outputis traded,anda nontradable servicessectorto examinetheimplications ofincreasing
North-Southtradeinnancialassets. Park(1998)buildsamodelwithtradableandnontradableinvestment
and consumptiongoods. His model generatespositivecross-countrycorrelation ofaggregateoutput anda
cross-countrycorrelationofconsumptionwhichislowerthanthat ofoutput.
Ourmodel diers from previous studies in several respects. First, we analyze the implications of our
model foralloftheaggregatesthat characterizethequantityanomaly (output,consumption,employment,
and investment). Second, ourmodel assumesimperfect substitution betweendomestic and foreignoutput
of all sectors. This means that there is cross-hauling (simultaneous exports and imports of goods of the
same type) in all sectors. In thedata, there is cross-haulingat ne levelsof disaggregationin almost all
sectors. 2
Third, ourspecicationnests standardinternationalbusiness cycle modelssuch asthe oneused
byBKK. 3
Thisallowsustoanalyzetheimpactofmultiple sectorsontheinternationaltransmissionofthe
businesscyclerelativetootherchangesinspecication,suchasthedegreeofsubstitutionbetweendomestic
andforeignoutput, tradeinintermediategoods,capitaladjustmentcosts,etc.
3 The Model
Therearetwocountrieswithtwosectorsineacheconomy. Theoutputofagivensectorinagivencountryis
animperfectsubstitutefortheoutputsofthecorrespondingsectorsinothercountries,sothatinequilibrium
eachcountrywillproducesomeofeachgood. WeuseArmington(1969)aggregatorstoamalgamatedomestic
andforeignproductionofagiventypeofgood. Then,thecompositeintermediategoodfromeachsectorcan 2
Inour view,thismakesthedistinctionbetweentradableandnontradablegoodsarbitraryanddiÆculttocalibratefrom thedata.
3
Thenesting isnotperfect, sinceweuse capitaladjustment costsratherthan time-to-buildasinBKK. Wediscussthis furtherbelow.
goodsofdierenttypesareaggregatedtoformanalcompositegood,whichiseitherconsumedorinvested
to form capital. Output is perishable if used for consumption or asan intermediate input, and durable
if used forinvestment. This structure is similar to that used in one-sector models, and is appropriatefor
thelimiteddegreeofdisaggregation thatweusein ourmodel. Thestructure oftheproduction sideofthe
economyis summarizedinFigure3below. 4
Sincethereisonecompositenalgoodineachcountry,themodelusesastandardspecicationofagents'
preferences. 5
There arenorestrictionsontrade in ourmodel, and assetmarkets arecomplete, in contrast
tosomepreviouspapersthathaveattemptedtoexplainthequantityanomaly. Sincemarketsarecomplete,
competitive equilibrium is equivalentto an appropriately-dened social planningproblem. This is in fact
how wecalculate the equilibrium allocations in oursimulations. However,for the purposes of calibrating
themodelusingitssteadystatepropertieswepresentanddiscusstheobjectivesandconstraintsofdierent
typesofeconomicagentsinthemodel. Firmsproduceoutputsbypurchasinglaborservicesandintermediate
inputsandbyrentingcapitalfromhouseholds. Innitely-livedhouseholdssupplylaborandcapitaltorms
andsolveintertemporalmaximizationproblems. ImportbrokerswhoseproductionfunctionsareArmington
aggregatorsamalgamatedomestic andforeignoutputofagiventypeofgood. FinalgoodsbrokersuseCES
aggregatorstoproduceonehomogeneousnalgoodpercountry,whichispurchasedbyhouseholdsandused
forconsumptionandinvestment. 4
ThankstoMartinBoileauforprovidingtherstdraftofthisgure. 5
TheArmington aggregator and the nal goodsaggregators couldeasilybereinterpretedas re ectingpreferences for a varietyofdierentgoods. Thiswouldnotchangeourresultsconcerningtheinternationaltransmissionofshocks.
ThesectoralproductionfunctionsareCobb-Douglas 6
andaregivenby
Y pst =z pst N s pst K s pst 2 Y m=1 M sm psmt ; (1) with s + s + 2 X m=1 sm =1
sothat there are constant returnsto scale. Thep subscripts referto the country where production takes
place and thes subscriptsto the sectorortypeof good that is being produced. M refersto thequantity
of an intermediate good used in the production of good s. The order of the second and third subscripts
in M isimportant. Thesecondsubscript indicatesthesectorwheretheintermediateinput isused(in this
casesectors)andthethirdsubscriptindicates thesectorwhere theintermediateinputisproduced(inthis
casem). There aretwotypesof intermediategoods. Y isoutput, z is anexogenous productivity level,N
denotes hours worked, and K is thestock of capital. The coeÆcients in the production processes donot
havecountry-specicsubscripts: apartfrom temporarydivergencesacrosscountries ofthez's, allcountries
haveaccess tothesametechniquesofproduction. All quantities aremeasuredinpercapitaterms.
Firmssolvethestaticproblem
maxP pst Y pst w pt N pst (r pst +Æ)K pst 2 X m=1 P pmt M psmt ; (2) whereP ps
givestherelativepriceoftheoutputofthes th
sectorofcountrypmeasuredinunitsofaggregate
consumption. In the absence of transport costs, arbitrage will insure that this price is the same in all
countries. Since laborismobileacrosssectors,therealwageratew pt
iscommonto allsectors. Incontrast,
sincecapitalcannotbetransferredacrosssectorswithin theperiod,r pst
,therentalratenetofdepreciation
costsinsectors, canbedierentacrosssectors intheshortrun(butnotin thesteadystate). 6
TheArmingtonaggregatorsaregivenby F ust = us (X 1sut ;X 2sut )= " 2 X p=1 ! psu X (1 su) psut # 1 1 su ; (3) where F ust
isthe quantityofgoods usedin countryuforall purposes,and X psut
isthe quantityofgood
s produced in country p and used in country u. The value of ! psu
can be set to impose home-country
preferenceandsymmetryacrosscountries.Theparameter1= us
istheelasticityofsubstitutionbetweenany
ofthesgoodsproducedincountryp=1;2andusedbycountryu. With us
closetozerotheproductsare
closeto perfect substitutes. Thefollowingresourceconstraintsforgood sproduced bycountrypandused
bycountriesu=1;2,musthold:
2 X u=1 u X psut = p Y pst ; 8t; (4) where u
isthepopulationofcountryuwhich usesgoodsproducedincountrypand p
isthepopulation
ofcountrypwhichproducesgoods.
Therepresentativeimport brokerforsectorsin countryusolvesthestaticproblem
maxV ust " 2 X p=1 ! psu X (1 su ) psut # 1 1 su 2 X p=1 P pst X psut ; (5) whereV ust
isusedtodenotetherelativepriceofcompositegoodsincountryu.
3.3 Domestic Brokers
Domestic brokersbuy compositegoodsfrom the dierentsectors and aggregatethemtogether to produce
onenalgoodwhichisusedbyhouseholdsforthepurposesofconsumptionandinvestment. Thenalgoods
aggregatorsforeachcountryaregivenby
Y ut = u (Q u1t ;Q u2t )= " 2 X s=1 $ us Q (1 u) ust # 1 1 u ; (6)
Q ust F ust 2 X m=1 M umst : (7)
so that the amount of good F ust
not used as intermediate inputs becomes an input into the aggregator
function whichyieldsthenalgoodY ut
.
Domesticbrokersmaximizedomesticvalueaddedbysolvingthestaticprotmaximizationproblem
max " 2 X s=1 $ us Q (1 u) ust # 1 1 u 2 X s=1 V ust Q ust : (8) 3.4 Households
Householdsaretheonlyagentswhomustsolveanintertemporalmaximizationproblem. Therepresentative
householdincountryuhasaninniteplanninghorizonanditsutilityfunctionis givenby
U ut =E t 1 X j=1 j u(C u;t+j ;1 N u;t+j ) = 1 1 " u E t 1 X j=1 j h C u u;t+j ( 1 N u;t+j ) (1 u ) i 1 " u ; (9) whereC ut
isconsumptionofthehomogeneousnalgood,with0< u <1; 1 "<1andwhere N ut = S X s=1 N ust :
Themaximizationproblemfortherepresentativehouseholdofcountryucanbewrittenas
max 1 1 " u E t 0 @ 1 X j=0 j h C u u;t+j (1 N u;t+j ) (1 u) i 1 " u 1 A ; (10)
subjecttothesequenceofconstraints
C ut + 2 X s=1 I ust 1+ I ust K ust =w ut N ut + 2 X s=1 (r ust +Æ)K ust ; 8t; (11) K ust+1 =( 1 Æ)K ust +I ust ; 8t: (12)
ust
countriesandsectors. Thetotaltimeendowmentperperiodisnormalizedtoequalone. Investmentissubject
toconvex(quadratic)costsofadjustmentwhichdependontheratioofgrossinvestmenttothecapitalstock
ineachsector. Werestrictthecostofadjustmentparametertobethesameinallsectorsandcountries. It
iswellknownthatin multi-countrymodelswithoutadjustmentcostsortime-to-build,investmentvolatility
ismuchtoovolatile. 7
3.5 Social Planning Problem
Thesocialplannermaximizesaweightedsumoftheutilitiesoftherepresentativeagentsofeachcountry. If
thejointstochasticprocessdeterminingthemodel'sforcingvariables(thetechnologylevelsintheproduction
functions) isstationary, thesocial planner'sproblem canbeexpressedasastationary discounteddynamic
programmingproblem. Thesocialplanner'svaluefunctionisgivenby
V(fz ujt g;fK ujt g)= max D E ( 2 X u=1 u u(C ut ;1 N ut )+EV( fz uj;t+1 g;fK uj;t+1 g) ) ; wherefz ujt gandfK ujt
garevectorswhoseelementsarerespectivelyalltheexogenousproductivityshocks
andthecapitalstocksinallcountriesandsectors. Therstsummationinsidethemaximandistheone-period
returnfunction ofthesocialplanner. Theutilityoftherepresentativeagentincountryuisweightedbythe
populationof countryu, sothat allagents in the model are treatedequally by thesocialplanner. If the
steady-statelevelsofthez uj
arethesameacrosscountries,thiswillensurethateachcountry'stradebalance
is zeroin the steadystate. E denotesthe mathematicalexpectationsoperatorconditional on information
available at time t, and D is the vectorof the social planner's control variables, which we dene below.
Theproblem issubjecttothelawsofmotion ofthecapital stocksgivenin equation(12), andto thejoint 7
ut as C ut = u u1 (X 1sut ;X 2sut ) 2 X m=1 M pm1t ;:::; us (X 1sut ;X 2sut ) 2 X m=1 M pmst ! 2 X s=1 I ust 1+ I ust K ust ; (13)
andwhere,using equations(1)and (4),wereplaceX ps2t ,8p,8swith X ps2t = 1 2 z pst N s pst K s pst 2 Y m=1 M sm psmt 1 2 X ps1t :
With allthese substitutions,itcanreadilybeseenthatthesocialplanner'schoicevariablesare
D=fI t ;N t ;M t ;X t g; (14) with I =fI ust g; 8u;8s; N =fN ust g; 8u;8s; M =fM psmt g; 8p;8s;8m; X =fX ps1t g; 8p;8s:
We use the methodology rst developed by Kydland and Prescott (1982) and described in detail by
Hansenand Prescott(1995)in orderto simulate themodelnumerically. After themodel iscalibrated, we
solve numerically for its deterministic steady state. Then, weuse aquadratic approximationof the
one-period returnfunction in the neighborhoodof thedeterministic steadystate,which impliesthat thevalue
4.1 Steady State
Sincemanyoftheparametervalueswillbechosentopindownlong-runaveragesofvariablesin themodel,
itisconvenienttoanalyzethesteadystateofthemodel insomedetailatthis stage. Thesteady statecan
befoundbysolvingsimultaneouslyforacertainnumberofstaticanddynamiceÆciency conditionsaswell
asmarket clearingconditions. The eÆciency conditions canbefound by considering explicitly theutility
andprotmaximizationproblems ofhouseholdsandrms;weabstractfrom theseproblemswhenwesolve
themodelasasocialplanningproblem.
Wechooseunits sothattherelativepricesP pst
areallequaltoone in thesteadystate. Then,therst
orderconditionsforprotmaximizationbyrmsimply
s = wN ps Y ps ; (15) s = ( r ps +Æ)K ps Y ps ; (16) sm = M psm Y ps : (17)
Giveninformationoncostssharesoflabor,capital,andintermediateinputs,whichisavailablefromnational
accountsandinput-outputtables,theseconditionscanbeusedtopindowntheparametersoftheproduction
functions.
Werestricttheweights! psu
sothattherelativepricesV pst
arealsoequaltooneinthesteadystate. The
rstorderconditionsforprotmaximizationbyimport brokersimply
! psu =! 1su X us psu X us 1su : (18)
Imposing azeroprotconditionthenleadstothefollowingexpressionsforthe! psu : ! psu = 0 B @ X psu P p=1 X psu 1 C A us : (19)
us
pindownthevaluesofthe! psu
.
Solvingfortherstorder conditionsforprotmaximizationbydomesticbrokersandfollowingalineof
reasoningsimilartothatfortheimportbrokersleadsto thefollowingexpressionsforthe$ us : $ us = 0 B B @ Q us S P s=1 Q us 1 C C A u : (20)
Fromtherstorderconditionsforconsumptionand hoursitfollowsthat
1 u u = s (1 N u ) N us Y us C us ; 8s: (21)
Byrestrictingthenumberofhoursworkedinthesteadystateandthesteady-stateratioofconsumptionto
output, this pins down the i
parameters. Thedynamic eÆciency conditionsfor the allocation of capital
imply r us =r= 1 1; (22) where ther us
are therental ratesofcapital incountryuandsectors. Wecanuse thisdynamic eÆciency
conditioneithertosolveforthesubjectivediscountrategiventherealrental rateofcapital,orviceversa.
4.2 Base-Case Parameter Values
The parametervaluesused forthe base-case simulationsare summarized in Table 1below. The model is
calibrated to quarterly data. Inorder to isolate therole ofsectoral shocksand intermediate goods in the
international transmission of the business cycle from other factors, we impose symmetry across the two
countries andsectorssothat
us =; 8u;8s; u =; u=1;2;
u
" u
="; u=1;2:
Wenormalizethepopulationineachcountryto equalone. Theparametervaluescalibratedfrom longrun
averagesin thedataareasfollows.
Theweightsoncapitaland laborintheproductionfunctionsare standard. Theyensurethatlabor's
andcapital'sshare ofnationalincomematch theaveragevaluesin thedata.
Weset thetotalweightonintermediategoods in theproductionfunctions to0.5, which matchesthe
averagevaluefromU.S.input-outputtables.
Wechoosethevalueof sothathouseholdsallocateonethirdof theirdiscretionarytimeperperiod
to leisure.
TheaverageshareofimportedversusdomesticallyproducedgoodsfromtheU.S.input-outputtables
givesus X 1s1 =X 2s2 =0:85;s=1;2; X 1s2 =X 2s1 =0:15; s=1;2:
Thetotalproductionofeachtypeofgoodisnormalizedtoequalonebyasuitablechoiceofthe
steady-statelevelsofthez pst
. Importsharesre ectastrongdegreeofhomepreference,with85%ofdomestic
productionofalltypesofgoodsconsumeddomestically.
The remaining parameters of the model are the depreciation rate of capital Æ, the adjustment cost
parameter , the elasticity of substitution parameters us
and u
, the preference parameters " u
, and the
parametersofthemultivariatestochasticprocessgoverningtheevolutionoftheproductivityvariables z us
(1995)in ordertofacilitatecomparisonwiththeirresults. Thevalueswerechosenasfollows.
Wesetastandardvalueforthedepreciationrate(Æ=0:025).
Weset theadjustmentcostparametersothat therelativevolatilityof aggregateinvestmentmatches
the data ( = 1:00) for the benchmark model economy. Cardia (1991) and Mendoza (1991) use a
similarapproach.
Wesetthevalueofthesubstitutionparametersin theArmingtonaggregators()togiveanelasticity
of 1.5 onthebasis ofpreviousstudies in the tradeliterature, notably Sternand Schumacher(1976),
Whalley(1985)andShiellsandReinert(1993).
Wesetthevalueofthesubstitutionparametersinthenalgoodsaggregators()togiveanelasticity
of0.9basedonWhalley(1985).
Wesetthevalueof" u
basedonstandardvaluesintheliterature. BKK(1995)usethesamevalue.
Wesettheaverageinterestrateto4%peryear,whichimpliesavalueof equalto 0.99.
The stochastic process generating the z us
's wascalibrated byestimating a rst-order vector
autore-gression(VAR),usingdataformanufacturingandnon-manufacturingoutputintheU.S.andagroup
ofEuropeancountries. 8
Theestimationresultsgive: 2 6 6 4 z 11;t+1 z 12;t+1 z 21;t+1 z 22;t+1 3 7 7 5 = 2 6 6 4 0:910 0:020 0:034 0:076 0:006 0:878 0:140 0:047 0:110 0:076 0:736 0:100 0:375 0:105 0:183 0:618 3 7 7 5 2 6 6 4 z 11t z 12t z 21t z 22t 3 7 7 5 + 2 6 6 4 11t+1 12t+1 21t+1 22t+1 3 7 7 5 : 8
2 6 6 4 1:000 0:174 0:084 0:204 0:174 1:000 0:230 0:081 0:084 0:230 1:000 0:189 0:204 0:081 0:189 1:000 3 7 7 5 ;
withpercentagestandarddeviationsequalto0.706,1.584,0.634and1.425.
4.3 GDP, Trade Balance and the Terms of Trade
Wecandene thefollowingaggregatevariables, which arenecessaryforcalculatingsomeofoursimulation
results.
Countryu'sGDPisgivenbythefollowingexpression:
GDP ut = u S X s=1 Y pst @ ps @X psut @ s @Q ust pi u S X s=1 S X m=1 M usmt @ u @Q ust : (23)
GDP is calculatedbysummingupthe valueaddedin eachsectorof theeconomy, measuredin units
of aggregate consumption. Sectoral output Y pst
is multiplied by the relative price @ps @Xpsu
to obtain
the value of output in sectors in terms of the composite home/foreign good u. Then, wemultiply
by the relativeprice @ u @Qust
which givesthe marginalcontribution of composite good uto aggregate
consumption. Wesubtract thevalue(in termsof aggregateconsumption)of theintermediateinputs
usedin allsectorsoftheeconomy. Thenumerairegoodistakentobeaggregateconsumption.
Thetradebalanceofcountryuis givenby:
B ut = H X p=1 u S X s=1 X psut @ ps @X psut @ u @Q ust H X p=1 i S X s=1 X psut @ ps @X psut @ u @Q ust : (24)
Onceagain,thevaluesofexportsandimportsaremeasuredintermsofunitsofaggregateconsumption
ofcountryu. Theexportsofeachsectortoallcountries aremultipliedby @ps @X
psu
in terms of thecomposite home/foreign good u, and then by @Q
us
to obtaintheir value in units of
aggregateconsumption. Imports from countrypof good s, X psut , aremultiplied by @ ps @X psu toobtain
theirvaluewhenusedincountryuintermsofthecompositegoodsandby @
u @Qus
toconverttounitsof
domesticaggregateconsumption. Theper-capitatradebalancecanbeobtainedbydividingtheabove
expressionby u
.
Thesectoraltermsoftradeforsectorsandbetweencountriesu
TOT ulst @ us @X usut 1 @ us @X lsut : (25)
WecalculatetherealexchangeratebetweencountriesuandlastheratiooftwoLaspeyresindicesof
thepriceofoutputinthetwocountries:
R ER t = P s P ust X us = P s P us X us P s P lst X ls = P s P ls X ls ; (26) where the P: st
are therelativeprices ofthe dierentsectoral outputs, theP :s
arethe relative prices
in the steadystate,and theX :j
are thesectoraloutputs in thesteadystate. Forcountryj, thereal
exchange rate measures the relative price of imports to exports, as is standard in the international
nanceliterature. 9
5 Results
5.1 Base Case
Themain resultsfor thebase-casescenarioare presentedin Tables2and3. The resultsarebasedon200
replicationsofhistoriesof100quartersinlength. Wegeneratedhistoriesof165observationsandtruncated
therst65observationssothattheresultsdonotdependoninitialconditions. 10
Theguresinparentheses 9
BKKrefertothismeasureasthetermsoftrade. 10
replications. Theygivearoughindicationofthestatisticalsignicanceofthestatistics. Wereportstandard
deviations only for the base case scenarioin order to conserve space | the standard deviations are very
similaracrossmodelspecicationsandcalibrations. Forpurposesofcomparison,wealsoreportthepredicted
momentsfromtheBKKbenchmarkmodelinthethirdrowofeach table.
Therelativestandarddeviationsofvariablesandthedomesticcorrelationsofoutputwithitscomponents
andwithhoursworkedaremostlysimilartothosegeneratedbyclosed-economyrealbusiness cyclemodels.
However, the relative volatility of consumption is somewhat too low, which is common in multi-country
models due to the added risk sharing opportunities that such models embody. In addition, the model
generates a negative correlation between output and net exports (the trade balance), which is consistent
with the data. As is common in previous multi-country business cycle models, the volatility of the real
exchange rate is counterfactually low. It is in fact signicantly lower than the prediction of the BKK
benchmarktwo-goodmodel.
Thecross-countrycorrelations are signicantly dierent than those predicted bythe BKK benchmark
model. There isasignicantamountofpositivetransmissionofthebusiness cycle,withacrosscorrelation
of output levels equal to 0.30 in our base case. This cross correlation is higher than the average in the
Zimmermann(1995)datasetbut iswithinonestandarddeviationofthisnumber. Themodelresolvesonly
one partof the quantity anomaly, since it still predictsa cross-countrycorrelation of consumption levels
that is signicantly higher thanthe cross correlation of output. This is not surprising. Our specication
of preferencesis similar to that of theBKK benchmark, and thereis nothing in ourmodelwhich inhibits
risksharingby agentsin dierentcountries. Whilethecross-correlationsofinvestmentand ofemployment
predictedbythemodelarenegative,bothvaluesarewithinonestandarddeviationofzero,andbothvalues
that the model's predictions concerning the international transmission of the business cycle are broadly
compatiblewiththedatain allrespectsexceptthecross-countrycorrelationofconsumption. 11
5.2 SensitivityAnalysis
Sensitivityanalysis allowsustocheckontherobustnessoftheresultsandtopinpointwhichaspectsofour
modelareresponsibleforgeneratingapositiveinternationaltransmissionofthebusinesscycle. Wecanalso
assesstherelativeimpactofmultiplesectorscomparedtootherchangesinspecicationontheinternational
transmissionofthebusiness cycle.
TheelasticityofsubstitutionparametersintheArmingtonandnalgoodsaggregatorshaveonlyminor
eects on the results. Sensitivity results with respect to the u
parameters in the nal goods are not
shown. Resultsareshownin Tables2and3fortwodierentscenarioswithalowelasticityofsubstitution
betweendomestic andforeigngoodsin theArmingtonaggregators. Reducing theelasticityof substitution
by increasing makesthe internationaltransmission of thebusiness cycle morepositive, but the eect is
notalwaysmonotonic. Thecross-countrycorrelationofoutputincreasesto0.42asthevalueof increases
to1=0:15. Thecross-countrycorrelationofconsumptionrstincreasesto0.83asthevalueofincreasesto
1=0:5,and thendecreasesto0.66with=1=:15. Theeecton thecross-countrycorrelationofinvestment
is similar. It increases to 0.03 as the value of goes from 1/1.5 to 1/0.5, and then decreases again to
-0.21with =1=0:15. The eect on thecross correlationof investment isnot signicant, given the large
standarderrorassociated withthis statistic. Thereasonsforamorepositiveinternationaltransmissionof
the cycle as increases are intuitive. A positive shock to technology in one sectorincreases the demand
for the outputs of all other sectors in all countries, both asintermediateinputs in the sector aected by 11
OurresultsarecompatiblewiththeexistenceofaJ-curve,asinBackus,KehoeandKydland(1994).Thecontemporaneous correlationbetweentherealexchangerateandnetexportsisnegative,butispositivebetweennetexportsandthersteight lagsoftheexchangerate. Thehighestcorrelationisbetweennetexportsandthethirdlagoftherealexchangerate.
countries becomelesssubstitutable, thedemand shift hasagreaternal impactonthe quantities of these
goodsthat areproduced.
Ourresultsshowthatthesizeofadjustmentcostshasimportanteectsontheinternationaltransmission
ofthecycle. Thepredictedvolatilitiesofaggregatesarenotstronglyaected bythesize oftheadjustment
cost parameter , except for the volatilities of investment and the trade balance, which both decrease as
adjustment costsincrease. However,thecross-countrycorrelationsare quitesensitive. As increases,the
cross-country correlations of output, employment and investment increase (the eect on the latter is not
monotonic), and the cross-country correlation of consumption decreases slightly. These results are once
againintuitive. Asadjustmentcostsincrease,itbecomeslesseasytoshiftfactorsofproductiontowardsthe
sectorsandcountrieswheretheyaremostproductive. Thecrosscorrelationsareincreasinglydominatedby
thepositivespillovereect thatapositiveshockinonesectorhasonthedemand forgoodsofothersectors
andcountries.
Thetwoparameterswiththestrongestimpactontheinternationaltransmissionofthecyclearethecapital
depreciationrateÆandthedegreeofhomepreferencecapturedbytheshareofimportedversusdomestically
produced goods. As thedepreciationrate increases,andashomepreference becomeslesspronounced,the
international transmission of the cycle becomes more positive. With a depreciation rate of 100%, 12
the
cross correlation of output levels is almost as high asthat of consumption, and the cross correlations of
both investment and employment become strongly positive. The intuition for this result is clear. With
low depreciation, a negative shock to one sector reduces investment without substantially reducing the
capital stock. The marginalproductivity of capital remains fairly stable. With high depreciation, lower
investmenttranslatesdirectlyinto alowercapital stock,which raisesitsmarginalproductivitydrastically. 12
Thiscasecorrespondstotheclosed-economymodelanalyzedbyLongandPlosser(1983).Theyndthatinamodelwith 100%depreciation,uncorrelatedsectoralproductivityshockscanleadtopositivecomovementsinsectoraloutputs.
dierentials.
With no home preference (half of the total production of each type of good is exported), the results
are quitedramatic. Thecross-countrycorrelationof output levelsincreasesto 0.97,and thecross-country
correlationsofbothinvestmentandemploymentincreasetocounterfactuallyhighlevels. Thecross-country
correlationofconsumptionlevelsisnotsignicantlydierentfromone. Thelatterresultisintuitive. With
nohomepreference,theconsumptionpreferencesofthehomeandforeignagentareidentical,andwithrisk
sharingtheconsumption levelsof thetwoagentsare almostperfectly correlated. It isonlybecauseutility
also depends on leisure, which is anontradable good, that the correlation is less than perfect. The high
correlationofinvestmentseemsquitesurprising. Toexplainthis result,weexaminedtheimpulseresponses
ofdomesticandforeigninvestmenttoapositivedomesticproductivityshock. Domesticinvestmentincreases
substantiallyinresponsetoapositiveproductivityshock. Theincreaseispersistent,withamonotonicdecay
back to its steady statelevel. With no home preference, foreign investment also increases in response to
a domestic productivity shock. The size of the increase is small, but it is also persistent, with the same
monotonicdecreasetothesteadystate. Itisthequalitativesimilarityintheimpulseresponseswhichleads,
despitethedierencein thesize oftheresponses,tothehighcrosscorrelation.
In order to investigate the sensitivity of international transmission to the specication of production
technology,wetriedaseriesofsimulationsin whichwereplacetheCobb-Douglasproductionfunctionswith
nestedCESfunctions,withanelasticityofsubstitutionbetweenlaborandcapitalequalto1.0andan
elastic-ityofsubstitutionbetweenprimaryandintermediateinputsequalto0.5. 13
Theresultsforcrosscorrelations
aresimilartothosein thebasecase,exceptforemployment. Withalowerelasticityofsubstitutionbetween
primaryand intermediateinputs, thepositivecross-countrycorrelationof outputlevelsis accompaniedby 13
ThiscalibrationisinspiredbytheworkofWhalley(1985),whoassumesaLeontief-styleproductionfunction,withxed inputcoeÆcients on an aggregate of primary inputs(witha unitelasticity of substitution between capital and labor)and intermediategoods.
labor.
Wealso report simulation results for a scenario in which we remove the spillover eects in the
inter-national transmission of technology shocks. We do so by setting the o-diagonal elements of the matrix
of autoregressivecoeÆcients of our estimated VAR to zero. We set the diagonal elements equal to their
estimatedvalues. SectoralSolowresidualscanstillbecorrelated,bythisisnowduesolelytothe
contempo-raneouscorrelationsoftheinnovations. Relativevolatilitiesarenotgenerallyaected,asshowninTable2,
withtheexceptionsofthetrade balancewhichbecomesmorevolatile. Thecontemporaneouscorrelationof
therealexchangeratewithoutputbecomesmorepositive. Table3showsthattheinternationaltransmission
ofthecycle actuallybecomesmorepositive. Thecrosscorrelationof outputlevelsis notstrongly aected,
butthecrosscountrycorrelationsofinvestmentandemploymentbothbecomepositive. Inaddition,
remov-ing spillovereects reduces thepredicted crosscorrelationof consumption levels. These resultsshow that
modelling technology spilloversusing an estimated VAR may actually leadthe model to underpredict the
internationaltransmissionofthecycle.
ThespecicationofourmodeldiersfromthatoftheBKKbenchmarkprimarilybecauseitincorporates
both intermediate goods and multiple sectors. We simulated versions of the model without intermediate
goods and with only onesector in each country (both with and without intermediate goods) in order to
judge the relative contributions of these changes to our results. The results show that the introduction
of intermediate goods does not have strong eects on the predictions of the model. The cross-country
correlationsareverysimilarinbothversionsofthetwo-sectormodel(withandwithoutintermediategoods).
Thecross-countrycorrelationsarealsoverysimilarintheonesectormodelwithintermediatesandwithout
intermediates. 14
However,goingfromaone-sectorspecicationtoatwo-sectorspecicationleadstoamore 14
RotembergandWoodford(1995)showthatmodelsinmodelswithconstantreturnstoscaleinproduction,perfect com-petition,andnocapitaladjustmentcosts,productionfunctionsforgrossoutputcanbereplacedwithvalueaddedproduction
and employment. This resultcanbeexplainedby examiningtherelativeimpactof productivityshocks in
the one-sector and two-sectormodels. In theone-sector model, the country that benets from a positive
productivityshockdrawsproductiveresourcesfromabroad. Inthetwo-sectormodel,apositiveproductivity
shock in onesectorleadsto a ow ofresourcesbothfrom abroadand from other sectors within the same
country. Becausecross-sectoralcomovementswithincountriesarelesspositive,cross-countrycomovements
ofoutputandotheraggregatesaremorepositive.
Theone-sectormodelwithoutintermediategoodsisthespecicationofourmodelwhichisclosesttothe
BKKbenchmark. Thetwodieronlyin howtheadjustmentofcapitalis modelled. TheBKKbenchmark
uses time-to-build, while our specication imposes convex adjustment costs that depend on the rate of
grossinvestment. Withconvexadjustmentcosts,thecapital owsinducedbyproductivitydierentialsare
dampened because of the costs of installing new capital. With time-to-build, investment projectsdo not
come on line immediately. However, if productivity dierentials are persistent enough, they can lead to
capital owsthataremoremassivethaninthepresenceofadjustmentcosts. Consequently,oursingle-sector
modelgeneratesahighercross-countrycorrelationofoutputlevelsandcrosscorrelationsofinvestmentand
employmentthat arelessnegativethantheBKKbenchmark.
6 Conclusions
We havedevelopeda two-countrymulti-sectormodel of the business cycle. Our results show that such a
modeliscapableofgeneratingapositiveinternationaltransmissionofthebusinesscycle,withcross-country
correlationsof output, employment, and investmentthat arebroadlycompatible with thedata foralarge
groupofindustrialized countries. Oursensitivityanalysis showsthat theinternational transmissionofthe
functionswithnolossingenerality. The(relativelysmall)impactofintermediategoodsonthepredictionsofourmodelcan beexplainedbythepresenceofadjustmentcosts.
becomesmoreconsistentwith the data whendomestic and foreigngoods become lesssubstitutable, when
capitaladjustmentcostsarehigher,whendepreciationcostsarehigherandwhenthere isalowerdegreeof
homepreference. Thecross-countrycorrelationofemploymentisalsosensitivetotheelasticityofsubstitution
betweeninputsintheproductionfunctions.
ThechangeinmodelspecicationwithrespecttotheBKKbenchmarkthathasthethestrongesteects
ontheinternationaltransmissionofthebusinesscycleistheintroductionofmultiplesectors. Thepresenceof
intermediateinputsinproductionismuchlessimportant. Thetwo-sectormodelleadstosimilarpredictions
concerningcross-countrycorrelations,asthetotalweightonintermediategoodsintheproductionfunctions
variesbetween0.5andzero. Thepredictionsoftheone-sectorversionofthemodelforcross-country
corre-lationsarealsoverysimilarwithandwithoutintermediategoodsintheproductionfunctions. Usingconvex
adjustment costsrather thantime-to-buildalso makesthe internationaltransmissionof thebusiness cycle
morepositive,withaparticularlystrongeect onthecrosscorrelationsofinvestmentandemployment.
Thecross-countrycorrelationof consumptionpredictedbyourmodelremainsveryhigh. Weconjecture
that a satisfactory explanation of all aspects of the quantity anomaly will necessitate using models that
combine multiple sectors with other features such as market imperfections that limit risk sharing. Other
papers (for example Kehoe and Perri, 1996) show that reduced risk sharing can have important eects
on the cross-countrycorrelation of consumption, in addition to aecting thecross-countrycorrelations of
othervariables suchasoutputandinvestment. Ourresultsshowthat itispossibletobuild amodelofthe
internationalbusiness cycle that explainsmanyof thefeatures of thequantityanomaly, withoutimposing
restrictionsonrisksharingorthe owsof capitalacrossnationalborders.
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Benchmark ParametersValues Preferences DiscountFactor 0:99 ConsumptionShare 0:34 CurvatureParameter " 2:00 Technology LaborShare 0:32 CapitalShare 0:18
IntermediateGoodsShare 0:25
Depreciationrate Æ 0:025
InvestmentAdjustmentCosts 1:00 SteadyState HoursWorked N 0:33 Armington Aggregator (Imports)
ElasticityofSubstitution 1= 1:50 X 1s1 =Y 1s =X 2s2 =Y 2s ; s=1;2 0:85 X 1s2 =Y 1s =X 2s1 =Y 2s ; s=1;2 0:15
CES Aggregator (DomesticBrokers)
Simulation Results
St. Dev. (%) Relative St. Dev. Correlationwith Output
Y TB C I N e C I N TB e U.S. Data a 1.92 0.52 0.75 3.27 0.61 3.68 0.82 0.94 0.88 -0.37 -0.20 Cross-Country Average b 1.62 1.05 0.30 2.97 0.71 2.31 0.69 0.80 0.57 -0.32 -0.03 BKK Benchmark a 1.38 0.30 0.47 3.48 0.42 0.48 f 0.88 0.93 0.94 -0.64 0.49 Base Case c 2.64 0.20 0.52 2.84 0.35 0.06 0.92 0.96 0.93 -0.48 0.47 (0.27) (0.02) (0.04) (0.17) (0.02) (0.00) (0.22) (0.01) (0.02) (0.13) (0.12) Sensitivity Analysis d =0 2.89 0.50 0.45 3.46 0.42 0.03 0.87 0.95 0.95 -0.57 0.28 =2 2.64 0.19 0.50 2.55 0.36 0.07 0.95 0.97 0.97 -0.03 0.48 =1=0:15 2.88 0.52 0.48 3.18 0.38 0.07 0.97 0.95 0.98 -0.60 0.14 =1=0:5 2.73 0.41 0.52 2.37 0.40 0.03 0.87 0.94 0.90 0.73 0.70 Æ=0:5 2.45 0.58 0.91 0.94 0.11 0.13 0.99 0.98 0.78 0.40 0.39 Æ=1 2.86 0.69 0.91 1.01 0.01 0.01 0.99 0.96 0.97 0.36 0.35
CES Production Function
e
2.78 0.29 0.52 2.86 0.36 0.07 0.93 0.96 0.97 -0.42 0.36
NoHomePreference 2.19 0.20 0.60 2.23 0.32 0.50 0.93 0.94 0.90 0.38 0.06
No Spillover Eects 2.95 1.60 0.34 3.09 0.41 0.06 0.97 0.99 0.99 -0.03 0.72
No IntermediateGoods 1.32 0.12 0.52 2.80 0.36 0.14 0.93 0.96 0.93 -0.49 0.50
One Sector Model 2.76 0.60 0.52 4.09 0.38 0.17 0.90 0.87 0.93 -0.60 0.46
One Sector w/oIntermediates 1.36 0.21 0.55 2.72 0.37 0.26 0.94 0.95 0.94 -0.60 0.59
One Sector w/oIntermediates,=0
c
1.46 0.34 0.49 3.41 0.58 0.18 0.90 0.92 0.93 -0.63 0.47
One Sector w/oIntermediates,=2
c
1.30 0.15 0.60 2.39 0.30 0.32 0.96 0.96 0.94 -0.58 0.58
a: FromBackus,KehoeandKydland(1995).
b: FromZimmermann (1995).
c: ParametervaluesaredescribedinTable1andinthetext.
SimulationResults Cross-Correlations Y C I N U.S. Data a 0.66 0.51 0.53 0.33 Cross-Country Average b 0.24 0.14 0.16 0.21 BKK Benchmark a 0.02 0.77 -0.58 -0.54 Base Case c 0.32 0.78 -0.12 -0.05 (0.12) (0.06) (0.13) (0.14) Sensitivity Analysis d =0 0.24 0.82 -0.31 -0.08 =2 0.40 0.74 0.08 0.25 =1=0:15 0.42 0.66 -0.21 0.19 =1=0:5 0.22 0.83 0.03 -0.26 Æ=0:5 0.54 0.77 0.62 -0.54 Æ=1 0.63 0.80 0.78 0.27
CES Production Function e 0.48 0.84 0.02 0.53 No HomePreference 0.97 0.99 0.98 0.90 No Spillover Eects 0.32 0.40 0.15 0.32 NoIntermediate Goods 0.33 0.78 -0.15 -0.05 One-Sector Model 0.22 0.80 -0.63 -0.45 One Sector w/oIntermediates 0.24 0.75 -0.35 -0.40 One Sector w/oIntermediates,=0 0.12 0.79 -0.55 -0.52 One Sector w/oIntermediates,=2 0.29 0.72 -0.20 -0.36 a Seenotesto Table2. ThecorrelationsarebetweentheU.S.and Europe. b;c;d;e Seenotesto Table2.
Production Structure of Model
Country1 Country2
PrimaryFactors(N;K) PrimaryFactors(N;K)
? Q Q Q Q Q Q s? + ? Q Q Q Q Q Q s? +
SectoralOutputs SectoralOutputs Primary Inputs 6 3 6 Q Q Q Q Q Q k 6 3 6 Q Q Q Q Q Q k X X X X X X X X X X X X X X X z X X X X X X X X X X X X X X X z ? ? 9 9 ? ? IntermediateInputs Armington Aggregators
CompositeGoods CompositeGoods
@ @ @ @ R @ @ @ @ R Final Aggregators
CrossCorrelations 0:8 0:7 0:6 0:5 0:4 0:3 0:2 0:1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Outputcross-correlations 0 5 10 15 20 25 30 35 40 Occurrences ... .... ... .... ... ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... 0:8 0:7 0:6 0:5 0:4 0:3 0:2 0:1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Investmentcross-correlations 0 5 10 15 20 25 30 Occurrences ... .... ... ... ... .... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... .... ... .... ... ... 0:8 0:7 0:6 0:5 0:4 0:3 0:2 0:1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Consumptioncross-correlations 0 5 10 15 20 25 30 Occurrences ... .... ... .... ... .... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Employmentcross-correlations 0 5 10 15 20 25 30 Occurrences ... ... .... ... .... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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Trade Balance and Terms of Trade
0:8 0:7 0:6 0:5 0:4 0:3 0:2 0:1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Tradebalance{outputcorrelations
0 1 2 3 4 5 6 Occurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... ... .... ... .... ... .... ... .... .... .... .... .... .... .... .... 0:8 0:7 0:6 0:5 0:4 0:3 0:2 0:1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Termsoftrade{outputcorrelations
0 1 2 3 4 5 Occurrences ... .... ... .... ... .... ... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... ... .... ... .... ... .... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... .... .... .... .... .... .... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . .