FinanceandEconomicsDiscussionSeries

FederalReserveBoard,Washington,D.C.

ISSN1936-2854(Print)

ISSN2767-3898(Online)

DemandUncertainty,Selection,andTrade

ErickSager,OlgaA.Timoshenko

2024-042

Pleasecitethispaperas:

Sager,Erick,andOlgaA.Timoshenko(2024).“DemandUncertainty,Selection,andTrade,”FinanceandEconomicsDiscussionSeries2024-042.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2024.042

.

NOTE:StafworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.

DemandUncertainty,Selection,andTrade*

ErickSagert

FederalReserveBoard

OlgaA.Timoshenko?TempleUniversity

May16,2024

Abstract

Thispaperexaminestheroleofuncertaintyonelasticitiesoftrade且owswithre-specttovariabletradecostsinacanonicalmodeloftradewithmonopolisticcompe-titionandheterogeneous?rms.Weidentifytwochannelsthroughwhichuncertaintyimpactstrade:throughexportparticipationthresholds(theselectionefect)andthedistributionofshocksgoverningexportselection(thedispersionefect).Whiletheselectionefectdampenstradeelasticitiesunderuncertainty,thedispersionefectisambiguous.Wedevelopamethodologyforusingcustoms?rm-leveldatatoquantifytradeelasticitiesunderuncertainty,andthemagnitudeofeachofthetwochannelsthroughwhichuncertaintyimpactstrade.We?ndthatuncertaintyampli?estradeelasticities,onaverage,indicatingthatthedispersionefectofidiosyncratic?rm-levelshocksdominates–thoughtheefectisheterogeneousacrossindustries.Theoverallmagnitudeoftheendogenousselectionmechanismontradeelasticitiesissmall,indi-catingthatthemaindriversoftradeinthisclassoftrademodelsareoverwhelminglyincumbent?rms.

Keywords:Demanduncertainty,?rmsizedistribution,extensivemargin,selection,tradeelasticities,welfare.

JEL:F12,F13.

*WethankArevikGnutzmann-Mkrtchyan,MinaKim,LoganLewis,MartinLopez-Daneri,AndreKur-mann,PeterMorrow,NunoLimao,MoritzRitter,Andr/esRodr/lgues-Clare,InaSimonovska,BenWilliams,andYotoYotov,aswellasseminarparticipantsatDrexel,theGeorgeMasonUniversity,theUniversityofMaryland,TempleUniversity,BankofCanada,AsianMeetingoftheEconometricSocietyinEastandSoutheastAsia2023,CanadianEconomicAssociationsMeetings2018,BEROCInternationalEconomicsConference2018,SouthernEconomicAssociation88thAnnualMeetings2018,WashingtonAreaInterna-tionalTradeSymposium2018,1stMid-AtlanticTradeWorkshop2017,andMidwestInternationalTradeMeeting2017forvaluablecommentsanddiscussions.TheviewsexpressedhereinarethoseoftheauthorsandnotnecessarilythoseoftheFederalReserveBoardofGovernorsortheFederalReserveSystem.TheworkwassupportedinpartbythefacilitiesandstafoftheGeorgeWashingtonUniversityColonialOneHighPerformanceComputingInitiative.Thepaperpreviouslycirculatedunderthetitle“UncertaintyandTradeElasticities”.Firstversion:March2017.

t2001CStreetNW,WashingtonDC,20551,UnitedStates.E-mail:erick.r.sager@

?Correspondingauthor,TempleUniversity,DepartmentofEconomics,1115PolettWalk,Philadelphia,PA19122,UnitedStates.E-mail:olga.timoshenko@

1

1Introduction

Whenvariabletradecostsvary,notonlydoexistingexporterschangethesizeoftheirship-mentsabroad,butalsothesetofexportersvariesthroughentryandexit.Participationdecisionsforexporters–thatis,entryintoexportmarketsandthesubsequentdecisionofhowintensivelytoproduceandshipgoodstoforeigndestinations–isaconceptuallyandquantitativelyimportantdimensionoftrade,andfactorsafectingthesedecisionscanplayacentralroleindeterminingthesocialvalueoftradeforaneconomy.However,thebench-markframeworkformeasuringthegainsfromtradeconsidersaspecialsetofcircumstancessurroundingpotentialexporters’decisions:?rmshavecompleteinformationaboutthede-mandfortheirproductsinallforeignmarkets.Whilethisbenchmarkhaselucidatedcentralmechanismsthatdrivethegainsfromtrade,particularlytheroleofselection,lessisknownabouttheroleofselectionintheempiricallymorerelevantcaseunderwhich?rmsfacesomeamountofuncertaintyabouthowpro?tabletheirventureintoforeignmarketswillbe.

Inthispaper,weintroduceuncertaintyabout?rm-levelidiosyncraticdemandinforeignmarketsintoacanonicalmodeloftrade、ala

Melitz

(

2003

),andderivepredictionsofthemodelforthepartialelasticityoftradewithrespecttovariabletradecosts.Weshowthatregardlessofwhether?rmsfaceuncertaintyornot,thepartialtradeelasticityadmitsthesamefunctionalform–itequalsthe?rm-leveltradeelasticity(theintensivemargin)scaledbytheefectofendogenousselection(theextensivemargin).Wedemonstratethatwhileuncertaintyhasnoimpactontheintensivemargin,thesediferentassumptionsabout?rm-levelinformationdohaveanambiguousefectontheendogenousselectioncomponentofthepartialtradeelasticitythroughtheirefectonexportselectionthresholdsanddistributionsoftheexportselectionshocks.

Wethereforeidentifytwodistinctchannelsthroughwhichuncertaintyimpactspartialtradeelasticities:theselectionandthedispersionefects.First,demanduncertaintyintro-ducesawedgebetweenentrythresholdsinthetwoinformationenvironmentsthatcaptures?rms’expectationsabouttheunexpectedcomponentofidiosyncraticdemandshocks.Werefertothisefectastheselectioneectofuncertainty.Second,demanduncertaintyintro-ducesawedgebetweentheexportselectionshocksinthetwoinformationenvironmentsthatcapturesrealizationsoftheunexpectedcomponentofidiosyncraticdemandshocks.Werefertothisefectasthedispersioneectofuncertainty.Thesetwodistinctchannelsstemfromthefactthattheinformationenvironmenthasadirectimpactonthetypeofidiosyncraticshocks?rmstakeintoaccountwhenmakingexportdecisions.Undercompleteinforma-tion,thedecisionsarebasedonrealizationsofproductivityanddemandshocks,whileunderuncertainty?rmsmaketheirdecisionsbasedonproductivityandonlypartialinformationaboutdemand,namelyidiosyncraticexpectationsaboutdemandshocks.

2

Usingthepropertiesofthemodel,weshowthattheselectionefectofuncertaintydamp-ensthepartialtradeelasticityrelativetoacompleteinformationenvironment,whilethedispersionefectisambiguous.Wethereforeproceedbyusingthetheoreticalmodelwithde-manduncertaintytoderiveanempiricalmethodologythatquanti?estradeelasticities,andtodisentangletheselectionanddispersionefectsofuncertainty.Ourempiricalmethodologyisbasedonthemodel’spredictionthatexportquantitydependsonexportelectionshocks,acombinationofex-anteproductivityshocksandexpectationsaboutdemand,whileexportsalesdependonexportselectionshocksandarealizationofanunanticipatedcomponentofdemandshocks.Thispropertyofthemodelallowsustosimultaneouslyuseexportquantityandsalesdatatorecoverexportselectionshocksandthedispersionoftheunanticipatedcomponentofdemandshocks.

WeapplythemethodologytoBrazilian?rm-levelexportdatafortheperiodbetween1997and2000.We?ndthatrelativetothecompleteinformationenvironment,uncertaintyreducestradeelasticitiesbyanaverageof8%duetotheselectionefect,holdingallelseconstant.Whilethedispersionefectistheoreticallyambiguous,we?ndthatinaboutninetysevenpercentofobservationsthedispersionefectampli?estradeelasticitiesbutdoessobyasmallamount,holdingallelseconstant.

Overall,we?ndthatuncertaintyampli?estradeelasticitiesinabouteightypercentofobservations,butdoessobyasmallamount.Moreover,theefectisheterogeneousacrossproducts,withlargerampli?cationconcentratedamongmoresubstitutableproducts.Uncer-taintydampenstradeelasticitiesintwentypercentofobservations,andthedampeningefectisconcentratedamongproductswithlowelasticitiesofsubstitutionacrossvarieties.Theseresultsindicatethatthedispersionofexportselectionshocksisthedominantmechanismthroughwhichuncertaintyimpactstradeelasticitiesamongsubstitutableproducts,whiletheselectionefectofuncertaintyplaysalargerroleinadjustmentstotradecostsamonginelasticproducts.

Finally,inthemodelwithuncertaintytheendogenousselectionefectincreasestradeelas-ticitiesbyanaverageof2%relativetoabenchmarkwithnoendogenousselectionindicatingthatincumbent?rmsarethemaindriversoftradeadjustmentsinthisclassofmodels.

Thispaperisrelatedtoseveralstrandsoftheliteratureoninternationaltrade.First,thebenchmarkmodelisbasedon

Melitz

(2003)andisfurtherdevelopedinmanyin且uential

papers,suchas

Chaney

(2008),

Bernard,Redding,andSchott

(2010),

Arkolakis,Costinot,

andRodriguez-Clare

(2012),

MelitzandRedding

(2015)

.Agrowingbranchoftheliteraturehasdemonstratedthatmodelsincorporatinguncertaintyalongthelinesof

Jovanovic

(

1982

)arewellsuitedtomatchsalientpatternsofempiricallyobserved?rmbehaviorsuchas?rmgrowthasafunctionofageandsize(

Arkolakis,Papageorgiou,andTimoshenko

(2018)),?rm

3

productswitchingbehavior(

Timoshenko

(

2015b

)),and?rminputandoutputpricingbe-havior(

Bastos,Dias,andTimoshenko

(2018))

.Althoughmodelsthatfollowthebenchmarkhavefocusedondecomposingandmeasuringtradeelasticities,thenormativeimplicationsofmodelsthatincorporateuncertainty,particularlyformeasurementsoftradeelasticitiesarenotyetwellunderstood

.1

Intermsofdecomposingtradeelasticities,thispapershowsthatselectionintoexporting(andhencetheextensivemarginoftradeelasticity),dependsontheinformationstructurefacedby?rms.Previousworkhasshownthatthepartialelasticityoftradewithrespecttovariabletradecostscanbedecomposedintoanintensiveandanextensivemarginofadjustmentcomponents(

Chaney

(2008)),andthattheextensivemarginadjustmentcru

-ciallydependsonthedistributionalassumptionswithrespecttothesourcesof?rm-levelheterogeneity(

MelitzandRedding

(2015))

.

SagerandTimoshenko

(2019)characterizea

且exibledistributionthatwelldescribes?rm-levelheterogeneityand?ndtheextensivemar-gintradeelasticitytobesmall.Withrespecttotradeelasticitymeasurement,thispaperusesastructuralmodelwithalternativeassumptionsaboutinformationandspeci?es?rm-leveldatarequirementsnecessaryforidenti?cation.Existingworkfocusesonfullinformationbenchmarksthatestimatetradeelasticitiesusingaggregatetrade且owsandpricesdata(see

EatonandKortum

(2002)and

SimonovskaandWaugh

(2014))ortrade且owsandtarifdata

(CaliendoandParro

(2015))

.2

Thispaperrelatestoseveralrelatedpapersoninformationasymmetriesintrade.Themostcloselyrelatedpaperstothisoneare

Timoshenko

(

2015a

)and

DicksteinandMorales

(2018)

.Bothstudyinformationasymmetriesintradebyusingdataandtheorytoinferinformationavailableto?rmswhenmakingexportparticipationdecisions.Notably,thosepapersfocuson?rm-leveloutcomes,whilethispaper’sfocusismacroeconomicinscopeandthereforecomplementarytothispreviouswork.Speci?cally,thispaperusesinsightsaboutexportparticipationdecisionsfromthesepreviouspaperstounderstandtheaggregateimplicationsofimperfectinformationonchangesintrade且owsduetochangesinvariabletradecosts.Accordingly,thispapermakesassumptionsthatarecustomizedtocomputingtradeelasticities(suchasestimatingheterogeneityinshocksthatleadtosalesandquan-tityoutcomes)butdoesnotfocusonotherassumptionsthatcancharacterizetheextensivemarginoftrade(suchasheterogeneityin?xedcostsofexporting).Despitethediferencein

focus,thispaper’smodelcapturesthe?rm-levelrelationshipsfoundinthepreviouslitera-

1Anotableexceptionis

Arkolakis,Papageorgiou,andTimoshenko

(2018),whocharacterizeconstrained

e伍ciencyofamodelinwhich?rmslearnaboutdemandbutdonotengageininternationaltrade.

2Thisliteraturefurther?ndselasticitiesestimatedfromaggregatetrade且owsaresmallerthanthosees-timatedfromdisaggregatedindustry-leveldata(

ImbsandMejean

(2015)),andthatthereissubstantial

heterogeneityinbilateraltradeelasticitiesduetoheterogeneityincountries’industrialproduction(

Imbs

andMejean

(2017))

.

4

ture(

Timoshenko

(2015a)?ndsthatpastcontinuousexporthistorypredictscurrentexport

choice,and

DicksteinandMorales

(2018)?ndsthat?rm-levelsalesandindustryaverages

predictexportingforlarge?rmsbutnotforsmall?rms)because?rmsinourmodelthathavepositiveexanteinformationaboutproductivitylevelsaremorelikelytobelargeandexport.

Finally,thispaperrelatestootherrecentworkontradepolicyuncertainty.

Handley

andLimao

(2015)?ndthattradepolicyuncertaintylowersentryintoforeignmarketsby

reducingthevalueoftheexportparticipationthreshold,whilewe?ndtheoppositeresult.Thedistinctionarisesfromdiferencesinthetimingofwheninformationisrevealedto?rmsandtheoptionvalueofwaitingsuchtimingmayproduce.Inourframework,uncertaintyisrevealedafterentryandproductiondecisionshavebeenmade.Therefore,waitinghasnoimpactona?rm’sdecisionrelevantinformation.Incontrast,in

HandleyandLimao

(2015)

?rms?rstobservearealizationoftarifpolicyandthenmaketheirdecisions.

Handleyand

Limao

(2015)frameworkthereforefeaturestheoptionvalueofwaiting

.Firmscanconditiontheirentrydecisionsonarealizationofashockandonlyenterwhentherealizationofashockishighenough,amechanismabsentfromourframework.

Baley,Veldkamp,and

Waugh

(2020)developamodelinwhich?rmsexportmorewhenthereisgreateruncertainty

aboutthetermsoftradeinbilateraltraderelationships,whichcanalsobethoughtofastradepolicyuncertainty,yetthewelfareefectsareambiguousanddependonpreferences

.3

Therestofthepaperisorganizedasfollows.Section

2

presentsthetheoreticalframework.Section

3

characterizestheefectofuncertaintyontradeelasticities.Section

4

detailsourempiricalmethodologyforquantifyingtradeelasticitesinanenvironmentwithuncertainty.Section

5

describesourdataandpresentselasticityestimationresults.Section

6

performsacounterfactualanalysisoftradeelasticitiesinanenvironmentwithcompleteinformation.Section

7

concludes.Allproofs,derivations,androbustnesschecksarerelegatedtotheAppendix

.4

3Thereareotherpapersthatconsidertheefectsofinformationontrade.

BerginandLin

(2012)showthat

theentryofnewvarietiesincreasesatthetimeoftheannouncementofthefutureimplementationoftheEuropeanMonetaryUnion,suggestingthatchangesintheinformationavailableto?rmshaveimmediateconsequencesfor?rms’decisions;

Lewis

(2014)studiestheefectofexchangerateuncertaintyontrade;

Allen

(2014)showsthatinformationfrictionshelptoexplainpricevariationacrosslocations;

Fillatand

Garetto

(2015)showthataggregatedemand且uctuationscanexplainvariationinstockmarketreturns

betweenmultinationalandnon-multinational?rms.

4Appendix

A

providesadetaileddescriptionofthemodelwithuncertaintyandcompleteinformation.Ap-pendix

B

derivespropertiesoftheendogenousselectioncomponentofthepartialtradeelasticity.Appendix

C

detailsthestepsofthecounterfactualanalysis.Appendix

D

presentsrobustnessresultsaccountingforthemeasurementerrorinthequantitydata.

5

2TheoreticalFramework

Thissectionoutlinesourmaintheoreticalframeworkwhichwillserveasthestructuralbench-markforquantifyingtradeelasticitiesinamodelwithuncertainty.Weconsideraneconomicenvironmentinwhichheterogeneous?rmsexportproductstomonopolisticallycompetitivemarkets.Thisenvironmentissimilartothatin

Melitz

(

2003

)withanaddeddimension

ofdemanduncertaintyaccordingto

Jovanovic

(

1982

)asadaptedtoaheterogeneous?rmsframeworkby

Arkolakisetal.

(2018)

.Weassumeexogenousentryasin

Chaney

(2008)

.5

2.1Demand

ThereareNcountriesandKsectorsineachcountry.Eachcountryisindexedbyjandeachsectorisindexedbyk.

EachcountryispopulatedbyamassofLjidenticalconsumers.Eachconsumerwithincountryjownsanequalshareofdomestic?rmsandisendowedwithaunitoflaborthatisinelasticallysuppliedtothelabormarket.Thepreferencesofarepresentativeconsumerincountryjarerepresentedbyanestedconstantelasticityofsubstitutionutilityfunction

whereΩijkisthesetofvarietiesinsectorkconsumedincountryjoriginatingfromcountryi,cijk(ω)istheconsumptionofvarietyω∈Ωijk,Ekistheelasticityofsubstitutionacross

varietieswithinsectork,zk(ω)isthedemandshockforvarietyω∈Ωijk,andμkisthe

Cobb-DouglasutilityparameterforgoodsinsectorksuchthatΣ1μk=1.

Costminimizationyieldsastandardexpressionfortheoptimaldemandforvarietyω∈Ωijk,givenby

cijk(ω)=ezk(ω)pijk(ω)-EkYjkPjE-1,(2)

wherepijk(ω)isthepriceofvarietyω∈Ωijk,Yjkistotalexpendituresincountryjonvarietiesfromsectork,andPjkistheaggregatepriceindexincountryjinsectork

.6

2.2Supply

Eachvarietyω∈Ωijkissuppliedbyamonopolisticallycompetitive?rmfthathasaccesstoalinearproductiontechnologythattransformslaborintooutput,q=exp(za)l.Uponentry,

5AllderivationsarerelegatedtoAppendix

A.

6TheassumedCobb-Douglasutilityspeci?cationoverconsumptionbundlesacrosssectorsimpliesYjk=μkYj,whereYjisaggregateincomeincountryj.

6

a?rmfsellingfromcountryitocountryjinsectorkisendowedwithanidiosyncratic

laborproductivitylevelzijkandasetofidiosyncraticdestination-sectorspeci?cdemand

shocks,{z}j=1,...,N

.7

Eachdemandandsupplyshockspair(z,zijk)isdrawnfroma

jointdistributiontobecharacterizedlater.

Firmsfromcountryisellingoutputinsectorktocountryjface?xedcosts,fijk,andvariable‘iceberg’tradecosts,τijk.Fixedandvariablecostsaredenominatedinunitsoflabor,andwjdenotesthewagerateincountryj.

Each?rmcanpotentiallysupplyonevarietyofaproductfromeachsector.Firmsdecidewhichmarketstoexportto(theextensivemargindecision)andhowmuchtoexporttoeachofthechosenmarkets(theintensivemargindecision).Withoutlossofgenerality,weassumethat?rmschooseaquantitytoexport.Pricesaretheresultofmarketclearinggiventheexportedquantityofthevariety,andthenexportsalesarerealizedalongwithprices.

2.3InformationStructure

Weconsideranenvironmentwithcompleteinformationandanenvironmentwithuncertainty.

Intheenvironmentwithcompleteinformation,?rmsobserveallidiosyncraticshocks

beforemakingdecisions.Namely,?rmsobservetheirsupply,zijk,anddemand,z,shocks

beforedecidingwheretoexportandhowmuchtoexport.Denotethe?rm’sdecisionrelevant

exportselectionshockinthecompleteinformationenvironmentbyzik.Aswedemonstrate

below,zikisgivenby

zik=(Ek-1)zijk+z.(3)

Intheenvironmentwithuncertainty,?rmsdonotobserveallidiosyncraticshocksbeforemakingexportdecisions.Thetimingoftheinformationand?rm’sdecisionsfollows

Arkolakis

etal.

(2018)andisasfollows

.

1.First,?rmsobservetheirsupplysideshocks,zijk,andformexpectationsaboutdemand

shocks,E(zjzijk).

2.Next,?rmsdecidewhetherandwheretoexport,andhowmuchtoexporttothechosendestinations.

3.Productiontakesplaceandallthequantitiesareshipped;pricesclearindestinationmarkets.

7Theidiosyncraticdemandshocksarerealizedbyconsumers,butareapayofrelevantstateforthe?rms.Thus,when?rmsenter,theydrawtheirrealizationoftheidiosyncraticdemandofconsumersthatdeterminestheirsales.Following

Foster,Haltiwanger,andSyverson

(2008),whodocumentthatidiosyncratic?rm-level

demandshocks,ratherthanproductivity,accountforagreatervariationofsalesacross?rms,wefocusonthedemandshocksthatare?rmspeci?c.

7

4.Lastly,?rmsobservetheirsalesandinfertheirdemandshocks,z,fromtherealized

observationsofpricesandsales.

Denotethe?rm’sdecisionrelevantexportselectionshockintheenvironmentwithuncer-

taintybyzijk.Aswedemonstratebelow,zijkisgivenby

zijk=(∈k-1)zijk+E(zjzijk).(4)

Observefromequations(

3

)and(

4

),thatexportdecisionintheenvironmentwithun-certaintyarebasedonpartialinformationabouttherealizationofdemandshocks.Thisdiferenceleadstodiferentimplicationsregardingthemagnitudeofthepartialtradeelas-ticitieswithrespecttovariabletradecostsacrossinformationenvironments,andprovidesnovelinsightsintowhichdataaresuitedtostructurallyidentifythepartialtradeelasticitiesintheenvironmentwithuncertainty.

2.4ModelValidation

2.4.1TimingAssumption

Thetimingassumptionintheenvironmentwithuncertaintyimpliesthat?rms?rstproduceanddelivergoods,andreceivepaymentsforthosegoodsafterdelivery.Suchpost-shipmentpaymentmethod,commonlyreferredtoasexporter?nanceinthetrade?nanceliterature,isthemostwidespreadmethodof?nancingexporttransactions.The

IMF

(

2009

)reportsthatgloballyexporter?nanceaccountsfor42percentofexporttransactions.InthecontextofLatinAmericainparticular,

Ahn

(2015)?ndsthatexporter?nanceaccountsfor80to90

percentofthevalueofimporttransactionsinColombiaandChile.Whilewedonotattempttocontributetothetrade?nanceliteraturenordowemodelexportpaymentmethods,itsitreassuringthatthetimingofpaymentsimpliedbythemodelinthispaperisconsistentwithempiricalevidenceonexport?nance.

Inthecontextofthetradeliterature,thetimingassumptionintheenvironmentwithuncertaintyfollows

Jovanovic

(

1982

)asadaptedtoaheterogeneous?rmsframeworkby

Arko-

lakisetal.

(2018)

.Theframeworkof

Arkolakisetal.

(2018)(duetothetimingassumption

inparticular)hasbeenshowntobeabletopredictwithin?rmandexporterbehaviorsuchasgradualgrowthovertimeanddecliningwithagesurvivalrates(

Timoshenko,

2015a;

Ruhl

andWillis

,

2017

),ageandsizedependenceof?rmgrowthrates

Arkolakisetal.

(

2018

),andwithin?rmpricedynamics(

Bastosetal.,

2018

).Inthecontextofthisliterature,thegoalofthispaperistoexploretradeelasticitiespropertiesofademandprocessanduncertaintythathasalsobeenshowntodeliverpropertiesof?rmbehaviorthatareconsistentwithempiricalevidence.

8

2.4.2UncertaintyinDemand

Ourchoicetomodeluncertaintyindemandstemsfromthreerecentstrandsofresearch.First,theliteratureon?rmgrowthhasrobustlyrejectedthenotionthat?rmsoperateatoptimalscaleimmediatelyuponentry.Forinstance,

RuhlandWillis

(

2017

)?ndthatanewexporter’sexportsalesgrowslowlyfollowingentryin?rm-levelColombianmanufacturingdata,takinganaverageoffouryearstocatchuptothe(unconditional)averageexporter.Learningmodelsdeliverthisfeatureofthedata,boththeoreticallyandquantitatively.Forexample,

Berman

etal.

(2019)?ndthatthelearningprocessgeneratestheempiricallyobserveddeclinein

?rms’salesgrowth,exitrates,andthevarianceofsalesgrowthwithinacohortconditionalonsurvivalinitsmarket.Moreover,

Fitzgeraldetal.

(2023)?ndthatlearningaboutdemand

explainsthedecliningexitsovertimeandtheobservedquantityandpricedynamicsintheirIrishexportdata.

Second,thecanonicalmodelinwhich?rmschoosetoexportbasedonproductivityhasbeenshowntobecounterfactual.Inparticular,incontrasttothecanonicalmodel’spre-dictionthatthesmallestexportershouldbelargerthanthelargestnon-exporter,

Eaton

etal.

(2011)and

ArmenterandKoren

(

2015

)?ndthatexportersandnon-exportersarenotstrictlysortedinthisway:thereisasigni?cantnumberofexportersthataresmallerthannon-exportersandnon-exportersthatarelargerthanexporters.Hence,

ArmenterandKoren

(2015)concludethatsize-independentvariationisneededtomatchtheobservedfrequency

andsizeofexporters.Inthispaper’smodel,expostrealizationsofdemandgeneratesuchsize-independentvariation.

Finally,recentempiricalevidencehasshownthatdemandshocksexplainalargefractionofthevariationin?rmsales.Forexample,

Hottmanetal.

(

2016

)haveshownthatvariationin?rms’productappealexplainsbetweenahalftotwo-thirdsofthevariancein?rmsales.

Eatonetal.

(2011)and

MunchandNguyen

(2014)useFrenchandDanishdata,respectively,

toestimatethat?rm-destinationidiosyncraticshocksaccountforalmosthalfofvariationinsales.Finally,

Fosteretal.

(2016)?ndthatdiferencesindemand,notproductivity,explain

sizediferencesbetweennewandincumbentplants.

2.5EnvironmentwithCompleteInformation

Inthecompleteinformationenv