Firm heterogeneity, comparative advantage and the transfer problem

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Firm heterogeneity, comparative advantage and the

transfer problem

Federico Trionfetti

To cite this version:

Federico Trionfetti. Firm heterogeneity, comparative advantage and the transfer problem.

Euro-pean Economic Review, Elsevier, 2018, 108, pp.246 - 258. �10.1016/j.euroecorev.2018.07.007�.

�hal-01921170�

Firm

heterogeneity,

comparative

advantage

and

the

transfer

problem

Federico

Trionfetti

1

Aix-Marseille Univ, CNRS, EHESS, Centrale Marseille, AMSE, France

a

b

s

t

r

a

c

t

Thispaper studies the transfer problem in a model featuring comparative advantage, mo- nopolistic competition, trade costs, and firm heterogeneity in factor intensity. The results arevery differentfrom those ofthe previousliterature. First, atransfercreates a secondary burden in situations where the neoclassical version of the Heckscher–Ohlin model would not. Second, a transfer affects wageinequality.Third, atransferisnotneutral toworld welfare. Fourth,floatingexchangeratesdo notsubstitutefor deflation.Fifth, asimulation

exerciseshowsthatthequantitativeeffectsoftradeimbalancesarecomparableinmagni-tudetothosearisingfrommajortrade agreements.

1. Introduction

“AftertheFirstWorldWareconomistsdiscussedtheeffectsofaunilateraltransfer-such asreparations-ontheterms of trade. And in the 1950s, as the endof the Marshall Plan comes into sight, economists must once again consider an identicalanalytic problem- thepossible effectsofa cessation ofunrequitedimports onthe termsof trade”.2 _{Inthe XXI}

century weareconfronted withanalytically similarproblemsarisingfromtransfersofvarious sorts;suchasthosearising fromtradeimbalances,fromtheintra-European transfers,fromforeignaid,andremittances.Some ofthesetransfers arise fromgovernmentaldecisions(e.g.,intraEuropeanUniontransfersandforeignaid),somearetheresultsofprivatedecisions (remittances),some are theresultsofinter-temporaloptimisation(e.g.,tradeimbalances)butall canbe studiedfromthe pointofviewoftheimpacttheyhaveontheeconomiesconcerned.Atransferhastwopossibleeffects.Oneistheprimary effect,orprimaryburden,whichconsistsintheresourcestobetransferred.Theotheristhesecondaryeffect,orsecondary burden, which consists in the generalequilibrium repercussions ofthe transfer on welfare.3 _{The existence of a primary}

burdenis,ofcourse, incontrovertiblewhilethe existenceandmagnitudeofthe secondaryburdenhas beentheobjectof contentionintheentireliterature ontheTransfer Problem.Asiswell known,thecontroversy overthesecondary burden hasbeensparkedoff byKeynes (1929) whofoundremarkablecommentatorsinOhlin (1929) andRueff (1929) .Theliterature

E-mail address: Federico.Trionfetti@univ-amu.fr

1 This paper is part of a research project funded by the Agence Nationale de la Recherche (France). Grant number ANR-12-GLOB-0 0 05-01. I thank Vera

Danilina for first class research assistance. I thank my department - Aix-Marseille School of Economics - for research funds that helped me carry out the simulation part of the project.

2_{Samuelson (1952, p. 278).}

3_{Keynes (1929) uses the term ‘Budgetary Problem’ to refer to the primary effect and ‘Transfer Problem’ to refer to the secondary effect. Samuelson}

flourishedwithcontributionsbyPigou (1932) ,andMetzler (1942, 1951) .Thisliteratureexaminedthepossiblerepercussions ofatransferonthedonortermsoftrade.Somearguedthatthedonortermsoftradewoulddeterioratethusgivingriseto asecondaryburdenforthedonor(thisview becameknownastheorthodox view),some arguedthat thedonortermsof trademightactually improvethusgivingrisetoasecondary benefitforthedonor(thesocalledanti-orthodoxview),and somearguedthatthetransferwouldbeneutralonthetermsoftrade.Samuelson (1952, 1954) markedamilestoneinthe literaturewhenhecametoclarifytheconditionsunderwhichtheorthodoxoranti-orthodoxviewisright.Laterworkstook intoaccountadditionalaspectssuchasthelinkbetweenstabilityandthetermsoftradeeffectsoftransfers(Johnson, 1956; Mundell, 1960; Galor and Polemarchakis, 1987 ), non-traded goods (McDougall, 1965; Dornbusch et al., 1977a ), multiple countries(Dixit, 1983; Yano 1983 ),manygoods(Balasko 1978 ),non-identicalpreferenceandnon-tradedgoods(Jones, 1970, 1975 ), investment-induced termsof trade effects (Djaji ´c et al., 1999 ). Though the modelassumptions becamericher the attentionremainedconcentratedonthetermsoftradeeffectsoftransfers.Thefocusonthetermsoftradewasnaturaland wellplacedsincetheconceptualframeworkusedbyallthisliteraturewastheonewenowcallthe“neoclassicalmodel” of trade.Inthismodel,theonlypossiblewaya transfercreatesasecondary burdenisviaanadverse changeinthetermsof trade.Samuelsonmakesthispointveryclearlyinhistwofamousarticles(1952,1954).

Ire-examine the Transfer Problem in the light ofmodels featuring factor proportions, monopolistic competition and heterogeneityinfirmfactorintensity.UsingthismodelIstudytheeffectofatransferonproductivity,incomedistribution andfactorallocation.Interestingly,theimportanceofsuchre-examinationhadnotescapedSamuelson’scrispanalysiswhen hewrote: “Only if one brings in Chamberlinian phenomenaof monopolistic competition dosubstantive effects arise, ...”

Samuelson (1954, p. 288) . Thislineofresearch wasnot pursued bySamuelson andremainedalmost entirelyunexplored evenaftertheappearanceandvastutilisationofmonopolisticcompetitionmodelsininternationaltradetheory.

Onlyafewpaperstookthisresearchdirection.Brakman and van Marrewijk (1995) werethefirsttouseamodelof mo-nopolisticcompetitiontostudytheeffectoftransfersintheformofaidtodevelopingcountries.Thekeyelementsintheir modelarenon-identicalpreferencesbetweencountriesandhomebiasedexpenditure.Theirmodelisasingle-factor, homo-geneousfirms,freetrademodelnotsuitabletostudythemattersIaddressinthispaper.Corsetti et al. (2013) useamodel ofmonopolisticcompetition,heterogeneousfirms,andapartitionofallfirmsinexportersandnon-exporters.Thispartition allowsthemtodistinguishbetweentheintensiveandextensivemarginoftradeaschannelsthroughwhichatransfermay affectwelfare.Theyfindthatthepresenceoftheextensivemarginattenuatestherepercussionsofthetransferonthereal exchangerateandonthetermsoftrade.Thisisbecausepartofthedemandchangesinducedbythetransferareabsorbed bytheextensivemargin.TheirapproachdiffersfrommineespeciallybecausetheyfocusonthetermsoftradewhileIstudy theeffectsoftransfersalsooninequality,productivity,relativepriceofgoods,andtheexchangerate.Asaresultofdifferent researchfocuses, their modeldiffersfrommineinthat itassumesnocomparative advantage,noselectionintoentry, un-biasedheterogeneity,andapartition betweenexportingandnon-exportingfirmsthatIdisposeofsinceitisnotnecessary formypurposes.Epifani and Gancia (2017) usea multi-country,two-sector,one-factormodelofmonopolisticcompetition where,likeinDavis (1998) ,thehomogeneous goodisnontraded andwhere theyinsertintermediate inputsinthesame wayasinKrugman and Venables (1995) .Intheirmodelatradesurplusmaybring aboutan appreciationoftheexchange rate,a terms-of-trade improvementandawelfare increase.The key elementsoftheir modelareintermediate inputsand tradecostinthehomogeneousgood.Theirmodeldiffersfrommineespeciallybecauseitdoesnotincludecomparative ad-vantageandheterogeneousfirms;assuchitisunsuitabletostudytheissuesrelatedtoproductivityandtheskillpremium thatIaddressinmystudy.Picard and Worrall (2015) alsostudytheeffectsoftransfers.Theystudywhetherthepossibility oftransfersbetweencountriesmakethecaseforacurrencyareastrongerorweaker.Theirnumericalsimulationsshowthat acurrency area isoptimalunderreasonableparametrisation ofthemodel.Theirwork, likemine, considerstransfers and alternativeexchangerateregimesbutdiffersfrommineintheresearch objectiveandinthemodelstructure.Their single-factor,monopolisticcompetitionmodelsufficestotheirpurposesbutdoesnottakeonboardmanyelementsIinsteadhave toconsider,such asfactorproportionsandfirm heterogeneity.Afewother papersare veryclosetomine intermsofthe modelbutarequitedifferentintermsoftheresearch objective.Bernard et al. (2007) ,Burstein and Vogel (2016) ;Costinot and Vogel (2010) andCrozet and Trionfetti (2013) alluseheterogeneousfirmsandcomparativeadvantage.However, differ-entlyfromthepresentpaper,thefirstpaperdoesnotallow forheterogeneity infactorintensityatfirmlevel,thesecond doesnotallowforentry,thethirdandfourtharemorecloselyrelatedbuttheydonotcontainflexibleexchangerates.Most ofall,thedifferencewiththesefourpapersisintheresearchobjectivesincenoneofthemstudiesthethetransferproblem. Theempiricalliteraturecountsonlythreepapers.Devereux and Smith (2007) provideanempiricalstudyontheeffectsof Franco–Prussianreparationpayments.Lane and Milesi-Ferretti (2004) provideevidencethatcountrieswithnetexternal lia-bilitiestendtohavedepreciatedrealexchangerates.Crinò and Epifani (2014) augmentthe(Dornbusch et al., 1977b )model withanon-tradedgood andfind,consistently withsuchmodel,that atrade surplus(atransfer) isassociated withlower skill-intensity ofdonorexports when thedonor isskill-abundant anda higher skill-intensityof donorexports when the donorisskill-scarce.4

The results ofmy studycontrast sharply withthose of the previous literature on the transfer problem. I findthat a transferbringsaboutadjustmentsinthetermsoftrade,inthedegreeofspecialisation,intheskillpremium,andinwelfare evenin situations wherethe previous literature found that a transferis neutralon the equilibrium. All theseeffects are

due,forthemostpart,toproductdifferentiation,comparativeadvantageandtradecosts.Heterogeneityinfactorintensityis responsibleforchangesonaverageproductivitywhosesigndependsontherelativefactorabundanceofthedonor. Further-more,whileinthepreviousliteratureatransferisneutralonworldwelfare,inmymodelitisnotbecausetransfer-induced productivitychangesaffectworldwelfare.Iaddresstheissueofflexibleversusfixedexchangerate.Intheearlyliteratureit wassuggestedthatafreelyfloatingexchangeratewouldeliminatetheeffectofatransferonnominalwages.Ifindthatin thepresenceofcomparativeadvantagesuchconclusionisincorrect.Toeliminatethefallinnominalwageitisnecessaryto expand themoneysupplyinthedonorcountry. Lastly,Icalibratethemodelandsimulatethe eliminationoftrade imbal-ancesbetweentheU.S.,theEuroAreaandChina.Ifindasecondaryburdenforthedeficit-donorcountriesandasecondary benefitforthe(only)surplus-recipientcountry(China).Theoverallwelfareeffectsarefoundtobecomparableinmagnitude tothoseofmajortradeagreements.

Tosumup, thehighlightsofthe modelare productdifferentiation, comparativeadvantage andheterogeneityinfactor intensity.Thehighlightsoftheresearchobjectivearetheconsequencesoftransfersontheskill-premium,productivity,and world welfare.The model is also able to shed new light on the old questions of devaluation versus deflation. Lastly, it providesaquantificationoftheeffectsofeliminatingtradeimbalances.

The remainder of the paperis as follows: Section 2 lays out the model, Section 3 discusses the general equilibrium andwelfareeffectsoftransfers,Section 4 revisitsthedeflationversusdevaluationdebate,Section 5 performsasimulation exercise,Section 6 concludesandtheappendixSection 7 completesthepaper.

2. Themodel

Theworldeconomyiscomposed oftwo countries,indexedbyc=A,B;endowedwithtwo factors,indexedby j=H,L; which produce two differentiated goods, indexed by i₌Y_,Z.5 _{Each country is endowed witha positive share}

_ν

c

j of the

world’s endowmentsdenotedHandL.Forconvenience,veryoftenIwillrefertoHasskilledlabourandtoLasunskilled labour.Internationaltradeissubjecttoicebergtradecosts bywhichforoneunitofgoodshippedonlyafraction

τ

∈[0,1] arrivesatitsdestination.

Technology. Productionrequires fixedandvariable inputsineachperiod. Thevariableinput technologytakesthe CES formhererepresentedbythemarginalcostwhich,forafirminindustryiofcountryc,is

mcc i

(

ξ

)

=



(

λ

i

)

σ

(

wcL

)

1−σ_[l

₍

_ξ

₎

_]σ−1₊

₍

₁₋

_λ

i

)

σ

(

wcH

)

1−σ_[h

₍

_ξ

₎

_]σ−1



1−1σ ₍₁₎

where

λ

i∈(0,1) isaconstant technologyparameterofindustry i,the variableswcH andwcL denote,respectively,the price

of H andL in country c, and

σ

_=1 measures the elasticity of substitution between factors. The variable

ξ

is a random variablewithcumulativedistributionG(

ξ

)andwithsupport(

ξ

0,∞)where

ξ

0>0.Thecontinuous,positive,increasing,and

differentiablefunctionsl(

ξ

)andh(

ξ

)contributetodeterminingfactorproductivity.Let

β

(

ξ

)≡ h(

ξ

)/l(

ξ

)bemonotonic.Iwill saythatheterogeneityisH-biasedif

β

(

ξ

)_>0;isL-biasedif

β

(

ξ

)_<0;isunbiasedif

β



(

ξ

)

₌0.

Firmsseeking toenterthe marketface fixedentrycosts. Paying thefixed entrycosts givestherightto draw

ξ

.Upon drawing

ξ

thefirm isabletocomputeits profit.Thefirmstaysinthemarketiftheprofitisnon-negativeandexits other-wise.Ifthefirm staysitremains attachedtoitsvalue of

ξ

untildeath dothempart.Atanypointintimeanyfirmhasa probabilityofdeathwhich,tosavenotation,issettobeequalto1.6 _GiventhatG(

_ξ

_{)andtheprobabilityofdeathare}

con-stantovertime,itisirrelevantfortheequilibriumwhetherthefirmdecidestostay onthebasisofexpectedprofitorthe basisofcurrentprofit.Let

ξ

_i∗cbethevalueof

ξ

inindustryiofcountrycforwhichtheprofitisequaltozero.Wemaythan define theaveragemarginalcost intheindustryasmcc_i≡

{

1

1−G(ξ∗c i ) ∞ ξ∗c i

(

mc c i

)

1−σdG

}

1

1−σ_,whichmaybemoreconveniently writtenas  mcc_i=



(

λ

i

)

σ

(

wcL

)

1−σ



_lc i

σ−1 +

(

1−

λ

i

)

σ

(

wcH

)

1−σ



_hc i

σ−1

1−1σ . (2) wherelc i ≡

(

1 1−G(ξ∗c i ) _∞ ξ∗c i

(

l

(

ξ

))

σ−1_dG

₎

σ1−1 andanalogouslyforhc

i.Thisdefinitionwillbeusedseveraltimesbelow.

Coming to fixed costs we may assume that they are homogenous or heterogenousacross firms.These alternative as-sumptionsgivequalitativelythesameresults.Iassumehomogeneousfixedcostssincethisassumptionallowstobefocused on heterogeneity in the productionprocess (which is the heart of thematter). Incidentally, thisis the assumption most commonlyadoptedintheliterature(Melitz, 2003; Bernard et al., 2007 ;andmanyothers).Specifically,Irepresentthefixed inputasahomogenous,non-traded,compositegoodproducedinaperfectlycompetitivemarketbyassemblinginaCESall thevarietiesofthedomesticindustryoutput.Accordingly,thecostofproducingoneunitoffixedinputcoincideswiththe average marginalcost describedin(2) .Thus, thefixed productioncost is_mcc_i where _is apositive constant; thefixed entrycostisemcci wheree isapositiveconstant.ThisspecificationisinspiredbyEthier(1980)butitmayalsobe

inter-pretedasinYeaple (2005) ,whoassumesthatthefixedcostisrepresentedbyoutputthatmustbeproducedbythefirmand

5 Product differentiation is based on Dixit–Stiglitz monopolistic competition but the economic mechanism it carries would remain unchanged if we used

other forms of product differentiations such as those à la Armington (1969) or Eaton and Kortum (2002) .

thatultimatelycannotbesold.ThedifferencewithYeaple (2005) isthatinthepresentmodeltheunitcostfunctionof un-saleableoutputismcc_i.Fixedcostsareproportionaltotheaveragemarginalcost.Aconvenientsimplificationobtainedfrom modellingfixedcosts inthiswayisthatthe averagefactorintensityintheindustryis independentofaggregateindustry output.

Demand.TherepresentativeconsumerhaspreferencesrepresentedbytheCobb-Douglasutilityfunctionu=

(

Y

)

γY

(

Z

)

γZ

where

γ

i∈(0, 1),

γ

Y+

γ

Z=1andwhereYandZ are CESaggregateswhose elasticityofsubstitution betweenvarietiesis

ς

>1.Gross domestic productis Ic_=wc

L

ν

LcL+wcH

ν

HcH.Factors ofproduction are taxed forthe solepurpose ofraising the

resources to be transferred. I assume per-capita taxation so as to rule out any direct distributional consequence of the transfer.LeterepresentstheunitsofA’scurrencyneededtopurchaseoneunit ofB’s currency.LetTbethetransferfrom

Ato Bdenominated inthe currency ofA. WhenT>0country Ais thedonor andBtherecipient, vice-versawhen T<0. Nationaldisposableincome,equaltoexpenditure,isthenEA_=IA_{− T forcountryAandE}B_=IB_+T/eforB.

Thedemandemanatingfromdomesticresidents,sA

id,andfromforeignresidents,sixA,inlocalcurrency fortheoutputof

afirminindustryiofcountryAis:

sA id

(

ξ

)

=



pA id

(

ξ

)

PA i



1−ς

γ

iEA sAix

(

ξ

)

=



pA ix

(

ξ

)

PB i



1−ς

γ

iEB, (3)

wheresstandsforsales,dfordomestic,andxforforeign;pA

id

(

ξ

)

andp A

ix

(

ξ

)

arethepricefacedbyconsumersandPicisthe

priceindex. Allpricesareexpressedinthecurrencyofthecountrywheretheyareconsumed.Analogousfunctionsobtain forsB

idandsBix.TotalfirmsalesarerepresentedbysAi

(

ξ

)

=sAid

(

ξ

)

+esAix

(

ξ

)

andsBi

(

ξ

)

=sBid

(

ξ

)

+sBix

(

ξ

)

/e.

Profitmaximizationandzeroprofit.Withmonopolisticcompetitionandunderthelarge-groupassumption,the profit-maximisingpricesforthedomesticandtheforeignmarketare:

pc id

(

ξ

)

=

ς

ς

− 1mc c i

(

ξ

)

, pAix

(

ξ

)

= pA id e

τ

, p B ix

(

ξ

)

= epB id

τ

(4) The notationmcc

i

(

ξ

)

reminds usthat firms withdifferent

ξ

have differentmarginal costs;they therefore apply different

pricesandwillhavedifferentsalesasaresult.Indeed,foranytwofirmswithdraws

ξ

and

ξ

therelativesalesare

sc i



ξ



sc i

(

ξ



)

=

mcc i



ξ



mcc i

(

ξ



)



1−ς . (5)

After drawing

ξ

a firm decides tostay inthemarket if

π

c

i

(

ξ

)

0anddecides toquitotherwise. Thus,recalling that the

firm’sprofitmaybewrittenas

π

c

i

(

ξ

)

=sci

(

ξ

)

/

ς

− mc c

i,thezeroprofitconditionis7

sc i



ξ

∗c i

=

ς

mcci. (6)

Aggregation.ApplyingEqs. (5) and(6) tosc

i

(

ξ

)

/sci

(

ξ

i∗c

)

givesthesalesofanyfirm asfunctionofthecutoff value

ξ

i∗c;

thatis:sc i

(

ξ

)

=



mcc i(ξ ) mc∗c i (ξi∗c)



1−ς

_ς

mcci.From thisexpressionwe obtaintheaveragesalesdefinedassci≡1−G1(ξ∗c

i ) _∞ ξ∗c i s c i

(

ξ

)

dG

which,usingtheaboveexpressionforsc

i

(

ξ

)

turnsouttobe sc_i=



 mcc_i mc∗c i

(

ξ

i∗c

)



1−ς

ς

mcc_i . (7)

Computingtheaverageprofitinindustryiofcountrycweobtain

π

c i =



sc_i

ς

− mcci



. (8)

Using(4) wemaycomputetheaveragedomesticprice,theaverageexportpriceandthepriceindices:

 pc_id=

_ς

ς

− 1mc c i, pAix= pA i e

τ

, p B ix= epB i

τ

, (9) PA i =



MA i



_ pA id

1−ς +MB i



_ pA ix

1−ς

1−1ς , (10) PB i =



MB i



 pB id

1−ς +MA i



 pB ix

1−ς

1−1ς , (11) whereMc i isthemassoffirms. 7 Since mc c

GeneralEquilibrium.Inadditiontoprofit-maximisingpricesandtothezeroprofitconditionsdiscussedabove,thereare fiveadditionalsets ofequilibriumconditions.First, stationarityofthe equilibriumrequiresthe massofpotentialentrants,

Mc

ei,tobesuchthatatanyinstantthemassofsuccessfulentrants,[1− G

(

ξ

i∗c

)

]Mceiequalsthemassofincumbentfirmswho

die,Mc i:



1− G



ξ

∗c i



Mc ei=Mci. (12)

Second,freeentryensuresthattheexpectedbenefitfromentryequalstheentrycost:



1− G



ξ

∗c i



π

c i=emcci . (13)

Theleft-hand-sideisthepresentvalue-priortoentry-oftheexpectedprofitandtheright-hand-sideistheentrycost. Third,we needto ensuregoodsmarket equilibrium. Computingtheaveragedemand from(3) we seethat average de-mandisequivalenttoreplacingtheaveragepriceintothedemandfunction,whichallowswritingthegoodsmarket equi-libriumequationsas sAi =sAid



pA id

+esA ix



 pA ix

, (14) sBi =sBid



_ pB_id

+sB_ix



pB_ix

/e. (15)

Fourth,equilibriuminfactormarketrequiresthattotalfactordemand,denotedLc

i andHic,beequaltofactorsupply

Lc

Y+LcZ=

ν

LcL, (16)

Hc

Y+HcZ=

ν

HcH. (17)

Lastly, two ‘quantitative’ money market equations assure that nominal money supply equates nominal money demand. Moneysupply equalsdomestic credit,Mc,plus reserves.A transferT>0depletes reserves inA andincreases reservesin

B.Likewise, mutatis mutandi,fora transferT<0.Thus,money supplyisMA− T andMB+T/e.Moneyis demandedonly fortransaction purposesandit is thereforeequalto disposable incomedivided by thevelocity.Iset thevelocity to 1to save notation. A transfer affects money demand becauseit affects disposable income. The money market equations are: MA− T=IA_{− T andM}B_+T/e=IB_{+T/ewhichsimplifyto}

MA =IA (18)

MB =IB_{. (19)}

After replacing Eqs. (9) and(10) –(8) into(13) –(17) andremembering that each ofthese isrequired to holdfor anyi

andanycwe can countequationsandunknownsforthetwo regimesoffixedandflexible exchangerate. FixedExchange Rate. Settinge=1 we count 11independent equilibrium conditionsand12 endogenous variables. The equationsare the fourfree-entryconditions(13) ,anythreeoutofthe fourgoods marketequilibriumconditions(14) and(15) ,andthe four factormarket equilibrium(16) and(17) . Theendogenousare

{

ξ

_i∗c

}

,

{

wc

L,wcH

}

and

{

Mic

}

.The equilibriumvalueofall other

endogenousvariablescanbecomputedfromthese.Inparticularunderfixedexchangeratethemoneysupplyisendogenous andsimplyadjuststoaccommodateanychangeinmoneydemand.Thechoiceofanumérairemakesthemodeldetermined. Thefixedexchangeratemodelis,afterall,apuretrademodel.FlexibleExchangeRate.SettingMAandMBequaltoexogenous constantsandlettingebeendogenouswecount13independentequilibriumconditionsand13endogenousvariables.The equilibriumconditionsarethe sameasinthefixedexchange rateregime plus thetwomoneymarket equations(18) and

(19) .The13endogenousarethesame12endogenousasinthefixedexchangerateregimeplustheexchangeratee. 3. Generalequilibriumeffectsoftransfers

The keyelementsinthe modelabove aredifferencesin factorproportions,productdifferentiation, andheterogeneous firms.Iwillstudytherole playedbyeach ofthiselementsingivingrisetotheeffectsofatransfer.Iwillbegin, however, bydiscussingtheeffectofatransferintheneoclassicalversionofthefactorproportionsmodeloftradesince thiswillbe thebenchmarkfromwhichourmodeldeparts.Throughoutthissectiontheexchangerateisfixedtounity.

3.1. Theneoclassicalbenchmark

ToobtaintheneoclassicalmodelfrommineallwehavetodoistoletYandZbehomogeneousgoods,G(

ξ

)bedegenerate sothat firmsare homogeneous,marketsbe perfectlycompetitive,andsetallfixed coststozero.Suchneoclassicalversion givesrisetothefollowingresult:

Proposition1. “Samuelsonneutralityproposition”.IntheneoclassicalmodeloftradewithidenticalCobb-Douglaspreferences atransferhasnoimpactonanyendogenousvariable.Therefore,thereisnotermsoftradeeffectandthereisnosecondaryburden.

Proof.SeeappendixSect. 7.1 . _

Samuelsonobtainsthisresultfirst ina modelwithouttradecosts (Samuelson 1952 ) andthen inthemodelwithtrade costs (Samuelson 1954 ).8 _{Inboth cases heobtains the resultin a modelwith fixed outputbut argues withcrystalclear}

logicthat thesameresultshouldobtain whenoutputmayvary. Thisintuitionisconfirmedformally inMundell’sfamous paperon thepure theory of internationaltrade (1960,Section 4 ) where,however,heonly proves it forthe caseof free trade.TocompletethepictureIproveinappendixSection 7.1 thatProposition 1 isvalidalsointhecaseofvariableoutput andcostly trade.It isusefulto recallheretheintuitionforProposition 1 .Thecaseofzerotradecostsis obvious:insuch caseconsumersfacethesameprice,givenidenticalpreferencesatransferhasnoimpactonrelativedemandforgoodsand thereforehasnoimpactontheequilibrium.Iftradecostsarepositiveconsumersindifferentcountriesfacedifferentprices buttheunitary elasticityofsubstitution makesthattheexpendituresharesare insensitivetosuchpricedifferences.Thus, thetransferisneutralalsointhepresenceoftradecosts.ThiswillnotbethecaseinthemodelIpropose.

Proposition 1 isan excellent starting point forour study becauseit ensures that any effectwe find when using our modelwillbe dueexclusively toits features;namely, productdifferentiation, biasedheterogeneity,andtheir interactions withfactorproportions.

3.2.Productdifferentiationandcomparativeadvantage

We nowresume the full modeldescribed inSection 2 andstudy theeffect oftransfers whenproduct differentiation isin the model.To thispurposeI keep the assumptionof firm homogeneity, i.e., a degenerate G(

ξ

). Ido not need firm homogeneitytoobtaintheresultsbutIprefertodiscussfirmheterogeneityseparatelyinthenextsub-sectionforclarityof exposition.

Byitsverynatureatransferreducesexpenditureinthedonorcountryandincreasesitintherecipientcountrythereby operatinganinternationalreallocationofexpenditure.Suchreallocationmaygiverisetoexcessesdemandandsupplywhich aretheonlychannelsthroughwhichatransfercanaffecttheinitialequilibrium.Indeed,theanalysisofthetransferproblem maybe posedasthe studyofthe changesin endogenousvariables requiredto eliminatethe excessdemand andsupply createdby thetransfer. Thisis why Ibegin my analysis by studyingthe effect of a transfer on the excessdemand and supplyforanyvariety.DifferentiatingEqs. (14) and(15) withrespecttoTaroundT=0givesustheexcessdemandwhichI expressinpercentagechangesanddenotedDˆc

i:9  DA i = −



1−

θ

2

_MB i



pB id

1−ς dT

θ

MA i



_ pA id

1−ς +



θ

2

ι

B₊

ι

A

_MB i



_ pB id

1−ς ≶0⇔dT≷0, (20)  DB i =



1−

θ

2

_MA i



_ pA id

1−ς dT

θ

MB i



pB id

1−ς +



θ

2

ι

A₊

ι

B

_MA i



pA id

1−ς ≷0⇔dT≷0, (21)

where

ι

c _{iscountry c’s share inworld disposable income and}

_θ

_≡

_τ

ς−1_{.Inspection of thesetwo equations leads to the}

followingproposition.

Proposition2. Atransfercreatesanexcesssupply(excessdemand)foranyvarietyofbothgoodsproducedbythedonor (recipi-ent).Thisleadstoadeterioration(improvement)ofthedonor(recipient)termsoftrade.

Proof.Expressions(20) and(21) . 

TounderstandProposition 2 consider, forinstance,a transferfromAto B.Thepropositionstatesthatthe transferwill createan excessdemandforanyvariety producedinBandanexcesssupplyforanyvariety producedinA.Thereasonis that -for anyvariety -foreign expenditureis smallerthan domestic expenditure sincetrade cost makethe priceof the foreign variety higher. Then, although a transfer gives rise to an increase in total expenditurein B equal to the decline inA, thedifference in theexpenditureshares creates an excesssupply forall A’s varietiesandan excess demandfor all

B’svarieties.10 _{A directconsequence is that theprice ofall varieties will declinein thedonor countryand willincrease}

inthe recipient country. This isa deterioration of the donorterms of trade.Proposition 2 showshow moving from the homogeneousgood andunitaryelasticityto Chamberlin (Dixit-Stiglitz)monopolisticcompetitiongives riseto substantive effectson the terms oftrade.Samuelson wasright. Butthere is a lotmore thanthe effect onthe terms oftrade when

8_{Samuelson (1954) , Table IV (p. 286), cell at the intersection of the row “Basic convention of unitary income elasticity and identical tastes” and the}

column “Real transport costs”; cell sub-case of elasticity of substitution between goods equal to 1 (Cobb–Douglas).

9 To make the prose lighter I will continue to use the term ‘transfer’ but since I am using comparative statics it is clear that I am referring to an

infinitesimally small transfer. A ∧ indicates percentage changes.

10 The net effect would be zero in the case of free trade ( _{θ= 1 ) or in the case of identical Cobb–Doublas preferences between varieties because in such}

factorproportionsareinthemodel.Thereasonisthattheexcessdemandandsupplyareingeneraldifferentforvarieties ofdifferentgoods.Thiscanbeseenbyusing(20) and(21) tocomputetheratiosDc

Y/DcZ andobservingthat

IfdT>0,then M A Y MA Z



 pB Zd

1−ς



_ pB Yd

1−ς  MB Y MB Z



pA Zd

1−ς



_ pA Yd

1−ς ⇒



DA Y  DA Z  1  DB Y  DB Z  1 (22) IfdT<0,then M B Y MB Z



 pA Zd

1−ς



_ pA Yd

1−ς  MA Y MA Z



 pB Zd

1−ς



_ pB Yd

1−ς ⇒



DA Y  DA Z  1  DB Y  DB Z  1 (23)

Thus,forinstance,theinequalitiesandimplicationsin(22) tellusthatatransferfromAtoB(i.e.T>0)whenAhasthe comparativeadvantageinY(asaconsequenceofwhichthesecondinequalityholdsas>)causesasmallerexcesssupplyfor

YthanforZinA(i.e.,DA

Y<0andDAZ<0butDAY/DAZ<1)andabiggerexcessdemandforYthanforZinB(i.e.,DBY> 0and



DB

Z>0butDYB/DBZ> 1).Analogously,atransferfromBtoA(T<0)whenBhasthecomparativeadvantageinYcausesDAY>0

andDA

Z>0 butDYA/DZA>1 andDYB<0andDZB<0butDYB/DBZ<1.Alltheother casesmaybe readanalogously.A transfer

fromtheskillabundanttotheskillscarce countrythenbrings aboutanincrease inthedemand forforYrelative toZ in bothcountries.ThiswillcauseanincreaseintherelativepriceofYandintheskillpremiumviaStolper-Samuelsoninboth countries.ToseethedifferencewiththeneoclassicalbenchmarkconsideracasewhereAisH-abundantandYisH-intensive. Insuchcase,ifwewereintheneoclassicalbenchmark,atransferfromAtoBwillbeneutralwhereasinthepresentmodel itbringsaboutadeteriorationofthetermsoftradeandanincreaseintherelativedemandforY.Oneotherwaytoseethe difference isthatintheneoclassicalbenchmarkthe termsoftradeandthe relativepriceofthegoodinwhichthe donor countryspecialisesareidentical.Inthepresentmodeltheyarenot.Thusadeteriorationofthetermsoftradeiscompatible withanimprovementintherelativepriceofthegoodinwhichthedonorcountryspecialises.Theinequalitiesabovelead tothefollowingproposition.

Proposition3. Atransfercausesinbothcountriesan increaseoftherelativedemandforthegoodinwhichthedonorcountry hasthecomparativeadvantage.Thishasthreeconsequences:

1. Anincreaseinbothcountriesintherelativepriceofthegoodinwhichthedonorcountryhasthecomparativeadvantage.

2. Anincreaseinbothcountriesintherelativepriceofthefactorwithwhichthedonorcountryisrelativelywellendowed.

3. Anincrease inbothcountriesin therelative massof varietiesof thegoodinwhichthedonor countryhasthecomparative advantage.

Proof. Directconsequenceof(22) –(23) . 

Productdifferentiationandcomparativeadvantageare bothnecessaryforProposition 3 .Ifwe remove comparative ad-vantagewhilekeepingmonopolisticcompetitiontheeffectsofProposition 3 vanishandweareleftonlywithProposition 2 , ifweremoveproductdifferentiationwhilekeepingcomparativeadvantagewearebacktoProposition 1 .11

3.3. Biasedheterogeneityandproductivity

Wenowresumefirmheterogeneity.Whenfirmsareheterogeneousinfactorintensityandentryisendogenousatransfer affectsproductivity.Toseethisitisconvenienttouse(7) and(8) towritethefreeentrycondition(13) asfollows:

_∞ ξ∗ i



_

mcc i

(

ξ

)

mc∗c_i

(

ξ

∗ i

)



1−ς − 1



dG

(

ξ

)

=e  . (24)

Unbiased heterogeneity means l

(

ξ

)

=h

(

ξ

)

whichimpliesthat factor pricescancel out of(24) .In such case, Eq. (24) de-termines

ξ

_i∗c independently of the rest ofthe model and, inparticular, independently of T. This implies that a transfer, thoughitimpactsonthepriceofgoodsandfactorsandonthemasses,hasnoimpactonproductivity.Whenheterogeneity is biasedinstead factorprices do not cancelout from themarginal cost ratio.In such situation thefree entry condition

(24) relates

ξ

_i∗ to factorprices and, throughthem, tothe transfer. Specificaly,when heterogeneityis biasedwe havethe followingrelationship:

d

ξ

_i∗c

d

ω

c 0 ⇔

β



₍

_ξ

₎

_{0 ∧}

_σ

_{1 (25)}

where

ω

c_{≡ w}c

H/wcL and∧ representpercentagechanges.SeeSection 7.2 forthemathematicalpassages.We maystatethe

effectofatransferonproductivityinthefollowingway:

11 In the absence of a comparative advantage M A

Y /M AZ = M BY /M BZ and  pAY d /  p A Zd =  p B Y d /  p B

Zdtherefore the excess demand is identical for all varieties of all goods in the same country as we see by inspection of (22) and (23) .

Proposition4. Whenfactorsaregrosssubstitutes,atransfercausesadecline(increase)inaverageproductivityofbothindustries inbothcountriesifthedonoris abundant(scarce) inthefactor towardswhichheterogeneityis biased.When factorsaregross complementtherelationshipisinverted.

Proof.Expression(25) 

Itisinterestingtounderstandtheeconomiclogicofexpression(25) .Consider,forinstanceatransferfromAtoBwhen

AisH-abundant,whichgivesrisetoanincreaseintheskillpremiuminbothcountries(i.e.,anincrease

ω

c_{).Sincefirmsare}

heterogeneousinskillintensitythey areaffecteddifferentlyevenwhen theyfacethesameincrease intheskillpremium. Specifically, highlyskill intensivefirms will lose competitivenesswithrespect to the least skillintensive firms since the formerusemore intensivelythefactor whoserelative pricehasincreased. Now,ifheterogeneity isskill-biased (

β

(t)>0) andfactors are grosssubstitutes (

σ

>1) then the leastskill intensivefirms willalso be the leastproductive firms.Their relativepositionimprovesandsomepreviously unprofitablefirmswillbecomeprofitableanddecidetostayinthemarket (i.e.

ξ

_i∗c declines).Proposition 4 restsonfactorproportionsandbiasedheterogeneity;intheabsenceofeitheronethereis noeffectonproductivity.12,13

3.4.Welfareeffects

Thewelfareeffectsoftransfers derivedirectlyfromthepropositionsabove.Contrarytotheneoclassicalbenchmark,the donorcountrybearsasecondaryburdenandtherecipientenjoysasecondarybenefit.Itiseasytounderstandthereasonfor thesewelfarechanges.Inthedonorcountryallpricesandwagesfallbutpartofexpendituregoestoforeignvarietieswhose increaseinpricecausesareductioninoverallpurchasingpowerofdonorcountryresidents.Likewise,mutatismutandi,for thewelfareeffectsofthetransferontherecipientcountrywelfare.Forthesamereasonsallfactorsbearasecondaryburden inthe donor country andenjoy a secondary benefit inthe recipient country. These welfarechanges donot leave world welfareunchanged,however,unlesscountrieshaveidenticalfactorproportions.Thereasonisthatwhenfactorproportions arenotidenticalatransferbringsaboutafalloranincreaseinproductivityinbothcountriesinaccordancetoProposition 4 . Worldwelfaredeclinesinthecaseofaproductivitylossandincreasesinthecaseofaproductivitygain.

4. Deflationversusdepreciation

Intheprevioussectionwereachedtheconclusionthatatransferinvolvesareductioninrealwagesinthedonorcountry. ThequestionIaddressinthissectionishowthisreductioninrealwagesistobeachieved:bydeflationorbydevaluation? Thereason forasking thisquestionisthat the politicalfeasibilityof thesetwo alternatives isvery different.Toputit in Keynes’words:“If[...]deflationisenforced,howwillthishelp?Onlyif,bycurtailingtheactivityofbusiness,itthrowsmen outof work,sothat, whena sufficientnumberofmillions areout ofwork, theywill thenaccept therequisite reduction intheirmoney-wages. Whetherthisispoliticallyandhumanlyfeasibleisanothermatter”.Keynes (1929) ,(p. 7).Wehave seenthemechanismdescribedbyKeynesintheprevioussectionswheretheonlydifferencewasthattheabsenceofprice rigiditiesmadethe realwage adjustmentinstantaneous. An alternativemethod toreduce realwages “wouldbe to allow theexchangevalue oftheGermanmarktofallby theamountrequiredtogive thenecessarybountyto exportsandthen toresistanyagitationtoraisemoney-wages”,(Keynes, 1929 ),(p. 6).Summingup,deflationrequiresfallingnominalwages whiledepreciation allegedly doesnot andthis makes itpolitically preferable.The choice betweenthesetwo alternatives arose alsoin recentEuropean policy debates whereexiting the Euro Areawas seenasan alternative to deflation.But is a floating exchange ratereally a substitutefor deflation?To address thisquestionI switch to the flexible exchange rate regime andresumeeasan endogenousvariable.Consider thecaseof atransfer fromAto B.Afall inthe exchangerate divertsdemandfromB’sto A’s varietiesthuscounteringthe excessdemandforB’s varietiesandtheexcesssupplyof A’s varietiescreatedbythetransfer.Willthisdepreciationeliminatethefallinnominalwage?Itwillifandonlyifitcanabsorb allexcessdemandandsupplygeneratedbythetransfer.Insuchcaseatransferhasnoother effectsthanthedepreciation ofthedonorcountry’scurrency.Ifinsteadthedepreciationcannotabsorballexcessdemandandsupplythenatransferwill havealltheeffectsstudiedintheprevioussectionincludingthefallinnominalwagesinthedonorcountry.Differentiating

Eqs. (14) and(15) withrespecttoTande(atT=0ande=1)weobtaintheexcessdemandgeneratedbythetransferand bytheexchangeratechange:

dDA i

(

pA id

)

1−ς =−

(

1−

θ

2

₎₍

_pB id

)

1−ς _MB i

γ

i

(

PA i

)

1−ς

(

P B i

)

1−ς dT +



θςγ

iIB

(

PB i

)

1−ς +



(

pB id

)

1−ς MiBIA

(

PA i

)

2(1−ς ) −

θ

(

pAid

)

1−ς MiAIB

(

PB i

)

2(1−ς )



θ

(

ς

− 1

)

γ

i



de (26)

12 In this model the relative price of a factor relates negatively to its relative abundance (see appendix _{Section 7.3 ). Proposition 4 , however, does not rest}

on such relationship. It rests on the effect that a transfer has on relative factor prices and, thereby, on productivity.

13 _{Crinò and Epifani (2014) find that larger trade surpluses are associated with lower average skill intensity of exports in skill-abundant countries (p.}

521). This evidence is perfectly in line with my theoretical results. Indeed a transfer from the skill abundant country (a larger trade surplus or lower trade deficit) results in a fall in ξ∗c

dDB i

(

pB id

)

1−ς =

(

1−

θ

2

)(

pAid

)

1−ς MAi

γ

i

(

PA i

)

1−ς

(

PiB

)

1−ς dT + −



θςγ

iIA

(

PA i

)

1−ς +



(

pA id

)

1−ς MAiIB

(

PB i

)

2(1−ς ) −

θ

(

p B id

)

1−ς MBiIA

(

PA i

)

2(1−ς )



θ

(

ς

− 1

)

γ

i



de (27)

A depreciation that absorbs all excess demand is a de such that dDc

i=0 for all i and c. It is clear by inspection of

(26)and(27) thatsuchsinglededoesnotexistsunlesscountrieshaveidenticalfactorendowments(proportions andsize). IffactorproportionsareidenticalthenMA

i =MiB≡ Mi,p_idA =pB_id,PiA=PiB,iffactorendowmentsareidenticalthenIA=IB≡ I

andexpressionsof(26) and(27) collapseto

Mi

γ

i dDA i =−

(

1−

θ

)

(

1+

θ

)

dT+

θ

[2

ς

−

(

1−

θ

)

]I

(

1+

θ

)

2 de (28) Mi

γ

i dDB i =

(

1−

θ

)

(

1+

θ

)

dT−

θ

[2

ς

−

(

1−

θ

)

]I

(

1+

θ

)

2 de. (29)

Insuchcaseadepreciationdeequaltothefollowingexpressionclearsallmarkets:

de=

(

1−

θ

2

)

θ

(

2

ς

− 1+

θ

)

dTAB

IA (30)

Inthiscasedeflationanddepreciationareperfectsubstitutes.Atransfercausesadepreciationofthedonor’scurrency and that isall.Real wagesfall butnominalwagesareunaffected. Furthermorethereare noother effectson theeconomy:no changein relativeprices, nochanges inproductivity,no changes inworld welfare.The transferrepercussionsare a zero-sum affairmediated by the exchange rate. If, instead, factor proportions are not the same then the excess demand and supplycreatedbythetransferdifferfordifferentcountriesandgoodsandthereforeadepreciationcannotclearallmarkets. Depreciationofthe donorcountrycurrency willoccur neverthelessbutwillbe accompaniedby fallingnominalwagesin thedonorcountry,increasingnominalwagesintherecipientcountry,andachangeintheskillpremiuminbothcountries. Insuchcasethecurrencydepreciationdoesnotsubstitutesfordeflation.Thus,thehopesthatfreelyfloatingexchangerates substitutefordeflationarenotwell-placed.

Proposition5. Unlesscountriesareidentical,depreciationcannotsubstitutefordeflation.

Proof. Inspectionof(26) and(27)  5. Theorywithnumbers

Wenowmovetoaquantitative exercisewherewesimulatetheeffectoftheeliminationofcurrentaccountimbalances betweentheU.S.,theEuro-Area,andChina.Eliminatingcurrentaccountimbalancesimpliesatransferfromthedeficittothe surpluscountry.Toperformsuch simulationIfollowtheapproachpopularised byDakle,Eaton andKortum(2007, 2008): I first calibratethe model and then Iuse the calibrated model to build a counter-factual. Althoughthe approach is the samemy modeldiffers grandlyfromtheirs.The quantitative implementationisalsodifferent.Inparticular, they simulate thesituationwheretradeimbalancesareeliminatedbytradeingoodsonly(leavingadegreeoffreedominservicetrade). Idon’tallowforthat.Moreover,theyallowforbilateraltradeimbalancestoremainwhileIsimulatethesituationinwhich all bilateral imbalances are zeroed. Twoother papers (citedbelow) simulatetheeffect oftransfers buttheir approachis differentinthatthey performadirectsimulationwithoutcalibratingthemodel.Parameter values,however,are conscien-tiously takenfromthedataorfromtheempiricalliterature. Althoughtheapproachinthesepapersislessdemandingon the modeltheresults areinformative andconstitute aprima facieevaluationofthe effectoftransfers. Alongtheselines (Epifani and Gancia, 2017 ) performnumericalsimulationsbasedon aonefactormodelcontaininganon-traded goodand intermediatedinputs.Theysimulatetheeffectofatradesurplusonthedonorcountry(atransferfromChinaorGermany intheirsimulations)butleaveunexploredtheissueofeliminating tradeimbalancesfortheother countries.Corsetti et al. (2013) performasimulationinaninter-temporalmodel.Theysimulatetheeffectofcurrentaccountimbalancesgenerated byinter-temporalshocktodemand,tosupply,orbyimperfectforesight.

FormyexerciseIneedtoparametrisethemodelandtomatchdata.Iassignto

σ

thevalue of2and3asoftenfound in gravity equations(see Head and Mayer, 2006 ,for an extensivediscussion). Iassume that G(

ξ

) isPareto andtake the shapeparametervaluefromBernard et al. (2003) whofindittobe3.7.14_{FollowingaconsolidatedpracticeIdefineskilled}

workers asworkers with tertiary education (see, e.g., Romalis, 2004 ; Costinot and Vogel, 2010 ). The relative abundance of skilled labouris measured by theeducational attainment reportedin Barro and Lee (2013) and Iassign values to

ν

c j

accordingly.15 _{The technologyparameters are}

λ

Y=4/10 and

λ

Z=6/10,which makeY skillintensiveandmatchthe data

14 The model in this paper gives rise to a gravity equation whose trade elasticity is _{σ− 1 . Thus, as in Crinò and Epifani (2014) I can assign to σand to}

the shape parameter the values found in the gravity literature.

Table 1

GDP and skill abundance.

United States Euro Area China GDP share 0.45 0.29 0.26 Skill abundance 0.268 0.1224 0.027

Table 2 Trade imbalances.

United States Euro Area China United States −0 . 55 −1 . 4

Euro Area −0 . 67

Table 3 Simulation results.

Eliminating bilateral trade imbalances All figures in percentage changes

United States Euro Area China

Average productivity in Y −0 . 0057 −0 . 0019 −0 . 0076

Average productivity in Z −0 . 0110 −0 . 0037 −0 . 0148

Secondary benefit for H −0 . 0618 0.0308 0.1504

Secondary benefit for L −0 . 0974 0.0177 0.1012

Secondary benefit for the country −0 . 0807 0.0209 0.1040

Nominal Exchange Rate of USD - 0.099 0.179 The neoclassical benchmark predicts no changes

reportedinRomalis (2004, Table 2) ,forthemanufacturingsector.Iassignto

τ

thevalueof0.8and0.6whichcorresponds toatradecostsof25%and67%ofvalueshipped.Theexpenditureshare

γ

Y issetat0.3. OtherparametervaluesareF=2

andFe=0.05.

Icalibrate the model to matchGDP shares andbilateral trade imbalances inpercentage of GDP. The data source for thesevalues isthe World Bank. I use thecalibrated model to simulatethe eliminationof all bilateral trade imbalances.

Tables 1 and2 reportdataonGDPshares,skillabundance,andtradesurpluses.Thetwotablescombinedshowthat elimi-natingtradeimbalancesrequirestransfersfromskillabundancetoskillscarcecountries.

Table 3 showsthe simulationresults.The table reportstheresults for

σ

=2 and

τ

=0.8.Simulations usingtheother combinationsofparametervaluesgaveresultsinthesameorderofmagnitude. Averageproductivitydeclinesinall coun-tries and industries in line with Proposition 4 . All factors bear a secondary burden in the donor country and enjoy a secondary benefitinthe recipient countryin linewithProposition 3 . Moreover, Hishurt lessthan Lin the donor-skill-abundantcountry(U.S.)andbenefitsmorethanLinthetworecipient-skill-scarcecountries(EuroArea andChina)inline withProposition 3 .

Iconcludethissectionwithasimple comparison.Tradeagreementsandtradeimbalancesoften‘compete’forspacein thenews.So,howimportantarethesefigurescomparedtothoseoftradeagreements?ArecentstudybyCaliendo and Parro (2015) estimatedthat asaconsequenceofNAFTA the cumulatedwelfareincrease fortheU.S.over theperiod1993–2005 wasof0.08%.Thisisalmost exactlyequaltothesimulatedwelfarelossfromeliminatingall tradeimbalancesreportedin

Table 3 .IftheU.S.tradedeficitkeepsthe currenttrendthiswelfareloss mayhappen inonlyacoupleofyears.Although thisisonly aroughcomparisonittells usthat thewelfareconsequencesoftradeimbalancesmaybeaslargeasthoseof majortradeagreements.

6. Summaryandconclusion

Thispaperrevisits thetransfer probleminthe light ofmodels featuring monopolisticcompetition andbiased hetero-geneity.Ihavefoundresultsthat areverydifferentfromthose intheprevious literatureandIhaveexplored issuesnever discussedbeforeinthecontextofthetransferproblem.

Thefirstsetofresultsshowthesynergybetweenbiasedheterogeneityandfactorproportionsingivingrisetotheeffects oftransfersonspecialisation,onfactorprices,andonproductivity.Thesecondsetofresultsconcernstheconsequencesofa transferoncountrywelfare,factorwelfare,worldwelfare,andoninequality.Thethirdsetofresultsconcernsthecomparison betweendeflation anddepreciation.The lastsetofresultsshowsthat hemagnitudeofthesecondaryeffects arisingfrom closingupcurrenttradeimbalancesiscomparabletothewelfareeffectsarisingfrommajortradeagreements.

7. Appendix

A1. Transfersintheneoclassicalbenchmark

Recall thatintheneoclassicalbenchmark YandZare homogeneousgoods,firmsarehomogenous,andthere isperfect competition.Tofixideas,andwithoutlossofgenerality,assume thatfactorintensitiesandfactorproportionsaresuchthat countryAisthe exporterofY.Toavoidnotationalconfusionletpic bethepriceofgoodi incountryc intheneoclassical

model.Transportcostsandtheexportpatternimplythefollowingpricerelationships:

pYB=

1

τ

pYA , pZA=

1

τ

pZB , (31)

Thegeneralequilibriumsystemiscomposedofthefollowingnineequations:

(

YA+YB/

τ

)

pYA



YA+Y_τB

pYA+



_ZA τ +YB

pZB =

γ

Y

(

IA− T

)

−

γ

Y

(

IB+T

)

IA+IB (32) pic=mcci , i=Y,Z; c=A,B. (33)

∂

mcc Y

∂

wc L Yc+

∂

mcc Z

∂

wc L Zc=

ν

LcL, c=A,B. (34)

∂

mcc Y

∂

wc H Yc+

∂

mcc Z

∂

wc H Zc=

ν

HcH , c=A,B. (35)

Eq. (32) ensures goods market clearing, Eq. (33) resultsfrom profitmaximisation, Eqs. (34) and(35) ensure equilibrium in factormarket. This system andthe choice of a numéraire determine the tenendogenous variables: four factorprices

{

wc

j

}

,twocommodity prices

{

pYA,pZB

}

,andfouroutputquantities{Yc,Zc}.Theimportantthingtonoticeisthatthetwo T

representingthetransfercanceleachotherout,seeEq. (32) .Thus,thetransferhasnoimpactonanyendogenousvariable. Thecrucialassumptionsforthisresultareidenticalpreferencesandunitaryelasticityofsubstitutionbetweengoods.Thisis theSamuelsonneutralitypropositionandourbenchmark.

Iftheelasticityofsubstitutionbetweengoodsisnotunitythenatransferisnotneutralanddoesnotcanceloutfromthe right-hand sideof(32) becausetheexpenditureshareswoulddifferbetweencountries.Asan example,replacetheCobb– Doublaswitha CESandan elasticityofsubstitution betweengoodsdenoted

ς

YZ.Then themarketclearingconditiontake

thesameformas(32) buttwodistinctexpenditureshares

γ

YAand

γ

YBreplacethecommonexpanditureshare

γ

Y:

(

YA+YB/

τ

)

pYA



YA+Y_τB

pYA+



ZA τ +YB

pZB =

γ

YA

(

IA− T

)

−

γ

YB

(

IB+T

)

IA+IB (36) where

γ

YA= p1−ς Y Z YA p1−ς Y Z YA +

τ

ς Y Z−1p 1−ς Y Z ZB (37)

γ

YB=

τ

ς Y Z−1_p1−ς Y Z YA

τ

ς Y Z−1_p1−ς Y Z YA +p 1−ς Y Z ZB (38)

TradecostsmakethatconsumersdonotfacethesamepriceindifferentcountriesandtheCESmakesthattheexpenditure shareis sensitiveto such pricedifference.Then, asstatedbySamuelson, thetransfer isnot neutral.There will beexcess demandandsupply,whichwillrequireatermsoftradeadjustment,thedirectionofwhichdependsonwhether

ς

YZislarger

orsmallerthanone.Inamode withfixedoutput thetermsoftradewilldothejob ofeliminating theexcessdemand,in amodelwithflexibleoutputtheoutputresponsecomestoattenuatethetermsoftraderesponsebutdoesnoteliminateit (Samuelson 1954 ,TableIVanddiscussioninpp.286–287).

A2. Mathematicalpassagesforinequality(25)

Totaldifferentiationofthefreeentrycondition(24) gives

0=



(

1−

ς

)



σ i

ω

1−σ _∞ ξ∗ i



hi/h∗i

σ−1 −



li/l∗i

σ−1



ω

1−σ_/h∗σ−1 i +



σi/li∗σ−1



2dG









ˆ

ω

11

+

⎧

⎪

⎨

⎪

⎩

(

1−

ς

)



l_i∗σ−1

ω

σ−1

ε

a∗ i +



σ ih∗iσ−1

ε

b∗ i



 _∞ ξ∗ i lσ−1 i ω σ−1+



σihσi−1



_l∗σ−1 i ω σ−1+



σ_ih∗_iσ−1

2dG

⎫

⎪

⎬

⎪

⎭







ϒc i,ξ∗ i 

ξ

∗ i (39)

where

ε

l_i≡ li

(

ξ

)

ξ

/li

(

ξ

)

,where

ε

h_i≡ hi

(

ξ

)

ξ

/bi

(

ξ

)

,andwhere



i≡

(

1−

λ

i

)

/

λ

iThesignsof

ϒ

ic,ξ∗

i and

ϒ

c i,ω are

ϒ

c i,ω 0 ⇔

β



(

ξ

)

0 ∧

σ

1 (40)

ϒ

c i,ξ∗ i <0 (41)

Fromwhich(25) followsdirectly.

A3.Factorproportionsandrelativefactorprices

Inthismodeltherelativepriceofafactorrelatesnegativelytoitsrelativeabundanceincostlytrade.Inournotationthis iswrittenasfollows:

ω

A_≷

_ω

B_⇔

_ν

A

H≷

ν

LA

∀

τ

∈

(

0,1

)

. (42)

Whiletotaldifferentiationshowsthisunequivocallyit nicerto showthatthisisindeedthecaseby thefollowingthought experiment.Assumethatfactorspriceequalisedincostlytrade.Then,from(39) anditsderivativeswe have

β

_i∗A=

β

∗B

i ,

∀

i.

Therefore,

mc∗A_i =mc∗B_i ⇒ mcAi =mc B

i ⇒ pAdi=pBdi. (43)

Underfactorspriceequalisationgoodsmarketsequilibriumequations(14) and(15) become



 mcA_i mc∗A_i



1−ς

ς

FimcAi =

γ

i IA MA i +

τ

σ−1MBi +

τ

σ−1

γ

iIB

τ

σ−1_MA i +MBi ,

∀

i (44)



_ mcBi mc∗B i



1−ς

ς

FimcBi =

τ

σ−1

_γ

_iIA MA i +

τ

σ−1MBi +

γ

iIB

τ

σ−1MA i +MBi ,

∀

i (45) LetLc

i andHic be average factors demandin each countryandindustry.As we knowthey obtain by applyingShepherd’s

lemmato the costfunction. Underfactors priceequalisation equalities(43) hold,thereforeLA

i =LBi =Li andHiA=HBi =Hi

andequilibriuminfactorsmarketsis



_ LYMYc+LZMcZ

=

v

c L¯L; c=A,B. (46)



_ HYMcY+HZMcZ

=

v

c HH¯; c=A,B. (47)

Using(43) inEqs. (44) and(45) andsolvinggivesMA

Y/MAZ=MBY/MZB.Thissolutioninthegoodsmarketequilibriumis

incon-sistentwithequilibriuminthefactorsmarket.Indeed,MA

Y/MAZ=MYB/MZBimpliesfrom(46) and(47) thattherelativedemand

forListhesameinbothcountries,butrelativesupplyisnot.Therefore,

ω

A₌

_ω

B_{is inconsistent with equilibrium in all}

mar-kets.Inwhichdirectionshouldfactorspricemovetoassureequilibriuminallmarkets?Thisiseasilyansweredbyobserving from(46) and(47) thatunderfactorpriceequalisationrelativedemandforLfallsshortofrelativesupplyinBandexceeds relativesupplyin A.Therefore

ω

A_/

_ω

B _{mustincrease. Thiswillmake allindustries becomemore H-intensive inAandless}

H-intensivein Bthuspushing towardstheequilibriuminfactors markets.Naturally, achangein factorspricealoneisnot sufficienttoassureequilibrium,asamatteroffactsanincreasein

ω

A_/

_ω

B_{pushesmarginalcostsindifferentdirectionsand}

requiresMA

Y/MAZ>MBY/MBZ forthe goods market equilibrium to be satisfied.Thus, a costly tradeequilibrium is necessarily

oneinwhich

ω

A_>

_ω

B _andMA

Y/MAZ>MYB/MBZ,whichisthecanonical Heckscher–Ohlinoutcome anditoccursinourmodel

forexactlythesamereasonsasinHeckscher–Ohlin.Afterall,thisisintuitivesinceourmodelstructuredoesnotviolateany ofthekeyassumptionsoftheHeckscher–Ohlinmodel.

Supplementarymaterial

Supplementarymaterialassociatedwiththisarticlecanbefound,intheonlineversion,atdoi:10.1016/j.euroecorev.2018. 07.007 .

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