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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

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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

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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.

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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 di erent 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.

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changesindemandforintermediateinputsproducedbythosesectors. Apositiveinter-sectoraltransmission

of productivity shocks in a closed-economy model could lead to a positive international transmission of

sectoralshocksinamulti-countrymodel.

We nd 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 di ersfrom othersin the literature. Inthe

thirdsection,wepresentourmodelanddescribehowtocalculateitscompetitiveequilibriumasthesolution

to asuitablesocial planningproblem. Inthefourthsection,wediscussthemodel's steadystateproperties

anditscalibration. Inthe fthsection, 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

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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-countrycorrelationsinthe rstrowofthetablearebetweenU.S.aggregatesandthecorresponding

aggregateinagroupofEuropeancountries. Thecross-countrycorrelationofconsumptionislowerthanthe

cross-countrycorrelationofoutput. Thecross-countrycorrelationof investmentisslightlyhigherthanthe

cross-country correlationof consumption, and thecross-countrycorrelation of employment is signi cantly

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 di erent aggregates. The gure shows that the mean values reported in

the second column of Table 3 mask a signi cant amount of variation across the countries in the sample.

Theordering implicitin thequantity anomalyis notrespectedfor allcountriesin thesample. Looking at

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leadsorlagsofupto fteen 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-countrymodelwithmoneyanddi eringratesoftrendproductivitygrowthacrosscountries. 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 speci cation of agents' preferences. Devereux, Gregory and Smith (1992)

developamodel withaparticulartypeof nonseparabilitybetweenconsumptionand leisure. Theysucceed

inloweringthecross-countrycorrelationofconsumption. StockmanandTesar(1995)introduceanontraded

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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

economyintoonesectorwhichproducesanintermediategoodandasingle nalgoodssector. The nalgoods

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 di erentiated intermediate goods and

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aprimarygoodssector(whoseoutputisusedasanintermediateinputinmanufacturing),amanufacturing

sectorwhose outputis traded,anda nontradable servicessectorto examinetheimplications ofincreasing

North-Southtradein nancialassets. Park(1998)buildsamodelwithtradableandnontradableinvestment

and consumptiongoods. His model generatespositivecross-countrycorrelation ofaggregateoutput anda

cross-countrycorrelationofconsumptionwhichislowerthanthat ofoutput.

Ourmodel di ers 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, ourspeci cationnests standardinternationalbusiness cycle modelssuch asthe oneused

byBKK. 3

Thisallowsustoanalyzetheimpactofmultiple sectorsontheinternationaltransmissionofthe

businesscyclerelativetootherchangesinspeci cation,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.

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goodsofdi erenttypesareaggregatedtoforma nalcompositegood,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

Sincethereisonecomposite nalgoodineachcountry,themodelusesastandardspeci cationofagents'

preferences. 5

There arenorestrictionsontrade in ourmodel, and assetmarkets arecomplete, in contrast

tosomepreviouspapersthathaveattemptedtoexplainthequantityanomaly. Sincemarketsarecomplete,

competitive equilibrium is equivalentto an appropriately-de ned social planningproblem. This is in fact

how wecalculate the equilibrium allocations in oursimulations. However,for the purposes of calibrating

themodelusingitssteadystatepropertieswepresentanddiscusstheobjectivesandconstraintsofdi erent

typesofeconomicagentsinthemodel. Firmsproduceoutputsbypurchasinglaborservicesandintermediate

inputsandbyrentingcapitalfromhouseholds. In nitely-livedhouseholdssupplylaborandcapitalto rms

andsolveintertemporalmaximizationproblems. ImportbrokerswhoseproductionfunctionsareArmington

aggregatorsamalgamatedomestic andforeignoutputofagiventypeofgood. FinalgoodsbrokersuseCES

aggregatorstoproduceonehomogeneous nalgoodpercountry,whichispurchasedbyhouseholdsandused

forconsumptionandinvestment. 4

ThankstoMartinBoileauforprovidingthe rstdraftofthis gure. 5

TheArmington aggregator and the nal goodsaggregators couldeasilybereinterpretedas re ectingpreferences for a varietyofdi erentgoods. Thiswouldnotchangeourresultsconcerningtheinternationaltransmissionofshocks.

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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-speci csubscripts: 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, canbedi erentacrosssectors intheshortrun(butnotin thesteadystate). 6

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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 di erentsectors and aggregatethemtogether to produce

one nalgoodwhichisusedbyhouseholdsforthepurposesofconsumptionandinvestment. The nalgoods

aggregatorsforeachcountryaregivenby

Y ut = u (Q u1t ;Q u2t )= " 2 X s=1 $ us Q (1 u) ust # 1 1 u ; (6)

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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 whichyieldsthe nalgoodY ut

.

Domesticbrokersmaximizedomesticvalueaddedbysolvingthestaticpro tmaximizationproblem

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

householdincountryuhasanin niteplanninghorizonanditsutilityfunctionis 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

isconsumptionofthehomogeneous nalgood,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)

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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. The rstsummationinsidethemaximandistheone-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 de ne below.

Theproblem issubjecttothelawsofmotion ofthecapital stocksgivenin equation(12), andto thejoint 7

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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

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4.1 Steady State

Sincemanyoftheparametervalueswillbechosentopindownlong-runaveragesofvariablesin themodel,

itisconvenienttoanalyzethesteadystateofthemodel insomedetailatthis stage. Thesteady statecan

befoundbysolvingsimultaneouslyforacertainnumberofstaticanddynamiceÆciency conditionsaswell

asmarket clearingconditions. The eÆciency conditions canbefound by considering explicitly theutility

andpro tmaximizationproblems ofhouseholdsand rms;weabstractfrom theseproblemswhenwesolve

themodelasasocialplanningproblem.

Wechooseunits sothattherelativepricesP pst

areallequaltoone in thesteadystate. Then,the rst

orderconditionsforpro tmaximizationby rmsimply

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

rstorderconditionsforpro tmaximizationbyimport brokersimply

! psu =! 1su X us psu X us 1su : (18)

Imposing azeropro tconditionthenleadstothefollowingexpressionsforthe! psu : ! psu = 0 B @ X psu P p=1 X psu 1 C A us : (19)

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us

pindownthevaluesofthe! psu

.

Solvingforthe rstorder conditionsforpro tmaximizationbydomesticbrokersandfollowingalineof

reasoningsimilartothatfortheimportbrokersleadsto thefollowingexpressionsforthe$ us : $ us = 0 B B @ Q us S P s=1 Q us 1 C C A  u : (20)

Fromthe rstorderconditionsforconsumptionand 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;

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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

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(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).

 Wesetthevalueofthesubstitutionparametersinthe nalgoodsaggregators()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

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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

Wecande ne 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

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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 di erentsectoral 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

the rst65observationssothattheresultsdonotdependoninitialconditions. 10

The guresinparentheses 9

BKKrefertothismeasureasthetermsoftrade. 10

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replications. Theygivearoughindicationofthestatisticalsigni canceofthestatistics. Wereportstandard

deviations only for the base case scenarioin order to conserve space | the standard deviations are very

similaracrossmodelspeci cationsandcalibrations. 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 signi cantly lower than the prediction of the BKK

benchmarktwo-goodmodel.

Thecross-countrycorrelations are signi cantly di erent than those predicted bythe BKK benchmark

model. There isasigni cantamountofpositivetransmissionofthebusiness 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 signi cantly higher thanthe cross correlation of output. This is not surprising. Our speci cation

of preferencesis similar to that of theBKK benchmark, and thereis nothing in ourmodelwhich inhibits

risksharingby agentsin di erentcountries. Whilethecross-correlationsofinvestmentand ofemployment

predictedbythemodelarenegative,bothvaluesarewithinonestandarddeviationofzero,andbothvalues

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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

assesstherelativeimpactofmultiplesectorscomparedtootherchangesinspeci cationontheinternational

transmissionofthebusiness cycle.

TheelasticityofsubstitutionparametersintheArmingtonand nalgoodsaggregatorshaveonlyminor

e ects on the results. Sensitivity results with respect to the  u

parameters in the nal goods are not

shown. Resultsareshownin Tables2and3fortwodi erentscenarioswithalowelasticityofsubstitution

betweendomestic andforeigngoodsin theArmingtonaggregators. Reducing theelasticityof substitution

by increasing makesthe internationaltransmission of thebusiness cycle morepositive, but the e ect is

notalwaysmonotonic. Thecross-countrycorrelationofoutputincreasesto0.42asthevalueof increases

to1=0:15. Thecross-countrycorrelationofconsumption rstincreasesto0.83asthevalueofincreasesto

1=0:5,and thendecreasesto0.66with=1=:15. Thee ecton 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 e ect on thecross correlationof investment isnot signi cant, 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 a ected by 11

OurresultsarecompatiblewiththeexistenceofaJ-curve,asinBackus,KehoeandKydland(1994).Thecontemporaneous correlationbetweentherealexchangerateandnetexportsisnegative,butispositivebetweennetexportsandthe rsteight lagsoftheexchangerate. Thehighestcorrelationisbetweennetexportsandthethirdlagoftherealexchangerate.

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countries becomelesssubstitutable, thedemand shift hasagreater nal impactonthe quantities of these

goodsthat areproduced.

Ourresultsshowthatthesizeofadjustmentcostshasimportante ectsontheinternationaltransmission

ofthecycle. Thepredictedvolatilitiesofaggregatesarenotstronglya ected 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 e ect on the latter is not

monotonic), and the cross-country correlation of consumption decreases slightly. These results are once

againintuitive. Asadjustmentcostsincrease,itbecomeslesseasytoshiftfactorsofproductiontowardsthe

sectorsandcountrieswheretheyaremostproductive. Thecrosscorrelationsareincreasinglydominatedby

thepositivespillovere ect 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).They ndthatinamodelwith 100%depreciation,uncorrelatedsectoralproductivityshockscanleadtopositivecomovementsinsectoraloutputs.

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di erentials.

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

correlationofconsumptionlevelsisnotsigni cantlydi erentfromone. 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,

despitethedi erencein thesize oftheresponses,tothehighcrosscorrelation.

In order to investigate the sensitivity of international transmission to the speci cation 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,with xed inputcoeÆcients on an aggregate of primary inputs(witha unitelasticity of substitution between capital and labor)and intermediategoods.

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labor.

Wealso report simulation results for a scenario in which we remove the spillover e ects 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. Relativevolatilitiesarenotgenerallya ected,asshowninTable2,

withtheexceptionsofthetrade balancewhichbecomesmorevolatile. Thecontemporaneouscorrelationof

therealexchangeratewithoutputbecomesmorepositive. Table3showsthattheinternationaltransmission

ofthecycle actuallybecomesmorepositive. Thecrosscorrelationof outputlevelsis notstrongly a ected,

butthecrosscountrycorrelationsofinvestmentandemploymentbothbecomepositive. Inaddition,

remov-ing spillovere ects reduces thepredicted crosscorrelationof consumption levels. These resultsshow that

modelling technology spilloversusing an estimated VAR may actually leadthe model to underpredict the

internationaltransmissionofthecycle.

Thespeci cationofourmodeldi ersfromthatoftheBKKbenchmarkprimarilybecauseitincorporates

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 e ects on the predictions of the model. The cross-country

correlationsareverysimilarinbothversionsofthetwo-sectormodel(withandwithoutintermediategoods).

Thecross-countrycorrelationsarealsoverysimilarintheonesectormodelwithintermediatesandwithout

intermediates. 14

However,goingfromaone-sectorspeci cationtoatwo-sectorspeci cationleadstoamore 14

RotembergandWoodford(1995)showthatmodelsinmodelswithconstantreturnstoscaleinproduction,perfect com-petition,andnocapitaladjustmentcosts,productionfunctionsforgrossoutputcanbereplacedwithvalueaddedproduction

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and employment. This resultcanbeexplainedby examiningtherelativeimpactof productivityshocks in

the one-sector and two-sectormodels. In theone-sector model, the country that bene ts 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-sectormodelwithoutintermediategoodsisthespeci cationofourmodelwhichisclosesttothe

BKKbenchmark. Thetwodi eronlyin howtheadjustmentofcapitalis modelled. TheBKKbenchmark

uses time-to-build, while our speci cation imposes convex adjustment costs that depend on the rate of

grossinvestment. Withconvexadjustmentcosts,thecapital owsinducedbyproductivitydi erentialsare

dampened because of the costs of installing new capital. With time-to-build, investment projectsdo not

come on line immediately. However, if productivity di erentials 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.

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becomesmoreconsistentwith the data whendomestic and foreigngoods become lesssubstitutable, when

capitaladjustmentcostsarehigher,whendepreciationcostsarehigherandwhenthere isalowerdegreeof

homepreference. Thecross-countrycorrelationofemploymentisalsosensitivetotheelasticityofsubstitution

betweeninputsintheproductionfunctions.

Thechangeinmodelspeci cationwithrespecttotheBKKbenchmarkthathasthethestrongeste ects

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,withaparticularlystronge ect 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 e ects

on the cross-countrycorrelation of consumption, in addition to a ecting thecross-countrycorrelations of

othervariables suchasoutputandinvestment. Ourresultsshowthat itispossibletobuild amodelofthe

internationalbusiness cycle that explainsmanyof thefeatures of thequantityanomaly, withoutimposing

restrictionsonrisksharingorthe owsof capitalacrossnationalborders.

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Costello, Donna and Jack Praschnik (1993), \Intermediate Goods and the Transmission of International BusinessCycles",mimeo, UniversityofWestern Ontario

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Hansen,GaryandEdwardPrescott(1995),\RecursiveMethodsforComputingEquilibriaofBusinessCycle Models" in Thomas F. Cooley, ed., Frontiers of Business Cycle Research (Princeton, NJ, Princeton UniversityPress)39-64

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Horvath,MichaelT.K.(1998),\CyclicalityandSectoralLinkages:AggregateFluctuationsfromIndependent SectoralShocks",Reviewof Economic Dynamics 1,781-808

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andSourceofInternationalComovement",mimeo, UniversityofCaliforniaatLosAngeles

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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)

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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 E ects 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.

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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 E ects 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.

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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

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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 ... .... ... .... ... .... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... .... ... .... ... ... 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 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 ... .... ... .... ... .... ... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... ... .... ... .... ... .... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... .... .... .... .... .... .... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Références

Documents relatifs

Non, l’homme aux lunettes épaisses ne voyait pas du tout ce qu’elle voulait dire mais heureusement pour Jeanne qui était à court d’idées, il ne voulait rien en laisser

Patients sans symptômes dans le territoire de la sténose..

This empirical methodology also allows us to identify the channel through which some variables affect bilateral trade (resp. bilateral holdings of financial assets): as

Secondly, the tariff cuts offered by the current EC proposal (the most critical proposal in tariff matters) protect food producers more than farmers: the post-Doha average tariffs

We also demonstrate that a minimal model with 15 modes, obtained from the truncated Euler equation, is able to capture the bifurcations of the large scale jets exhibited by

The higher occupation rates of nest boxes and similar egg-laying dates showed that artificial devices were preferred or equally selected by European rollers compared

The first step of the method consists in forming the similarity matrices. Several distance measurement exist, among which the Levensthein[23], the Jaro[24] and the Jaro-

policy, we provide necessary and sufficient conditions for it to be optimal for &#34;some&#34; agent with an increasing, strictly concave, time-additive, and state independent