NBER WORKING PAPER SERIES

COGNITIVE MOBILITY:LABOR MARKET RESPONSES TO SUPPLY SHOCKS IN THE SPACE OF IDEAS

George J. BorjasKirk B. Doran

Working Paper 18614http://www.nber.org/papers/w18614

NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

Cambridge, MA 02138December 2012

We are grateful to Patrick Ion, Graeme Fairweather, Norm Richert, and Erol Ozil from the AmericanMathematical Society for extensive collaboration and support in preparing the data. The authors aregrateful to the Upjohn Institute, the Kauffman Foundation, and the Sloan Foundation for their financialassistance. The findings reported in this paper did not result from a for-pay consulting relationship.The views expressed herein are those of the authors and do not necessarily reflect the views of theNational Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.

© 2012 by George J. Borjas and Kirk B. Doran. All rights reserved. Short sections of text, not to exceedtwo paragraphs, may be quoted without explicit permission provided that full credit, including © notice,is given to the source.

Cognitive Mobility: Labor Market Responses to Supply Shocks in the Space of IdeasGeorge J. Borjas and Kirk B. DoranNBER Working Paper No. 18614December 2012, Revised April 2013JEL No. J6,O31

ABSTRACT

Knowledge producers conducting research on a particular set of questions may respond to supply anddemand shocks by shifting resources to a different set of questions. Cognitive mobility measures thetransition from one location to another in idea space. We examine the cognitive mobility flows unleashedby the influx of Soviet mathematicians into the United States after the collapse of the Soviet Union.The data reveal that American mathematicians moved away from fields that received large numbersof Soviet émigrés. Diminishing returns in specific research areas, rather than beneficial human capitalspillovers, dominated the cognitive mobility decisions of knowledge producers.

George J. BorjasHarvard Kennedy School79 JFK StreetCambridge, MA 02138and NBERgborjas@harvard.edu

Kirk B. Doran438 Flanner HallUniversity of Notre DameNotre Dame, IN 46556kdoran@nd.edu

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Cognitive Mobility: Labor Market Responses to Supply Shocks in the Space of Ideas

George J. Borjas and Kirk B. Doran*

Cognitio:knowledgeasaconsequenceofperceptionoroftheexerciseofourmentalpowers;aconception,notion,idea

—CharltonT.LewisandCharlesShort,ANewLatinDictionary,1879

I. Introduction

BeginningwithSjaastad(1962),thestudyoflabormobilityhasbeenacentralarea

ofconcerninlaboreconomics.Therehavebeencountlessstudiesofthedeterminantsand

consequencesof,forexample,jobmobility,geographicmobility,andoccupationalmobility.

Thesestudiesaretypicallymotivatedbytheinsightthatmobilityplaysacentralrolein

allowinglabormarketstore‐equilibrateinresponsetosupplyanddemandshocks,

improvinglabormarketefficiency.

Thispaperintroducesandexaminestheeconomicsofadifferenttypeofmobility:

cognitivemobility.Wearguethatinresponsetoshocksworkersnotonlymovefromone

jobtoanother,orfromonegeographiclocationtoanother,butalsomoveinthemore

abstractspaceofideas.1 Knowledgeproducerswhoareconductingresearchonaparticular

*HarvardKennedySchoolandNationalBureauofEconomicResearch;andUniversityofNotreDame.

WearegratefultoRichardFreeman,DanielGoroff,DanielHamermesh,GordonHanson,BillKerr,SolomonPolachek,PaulaStephan,SarahTurner,tworeferees,andnumerousseminarparticipantsforcommentsonanearlierdraftofthispaper.WealsothankPatrickIon,GraemeFairweather,NormRichert,andErolOzilfromtheAmericanMathematicalSocietyforextensivecollaborationandsupportinpreparingthedata.WeacknowledgethefinancialassistanceprovidedbytheUpjohnInstitute,theKauffmanFoundation,andtheSloanFoundation.

1Thesocialsciencesliteratureonthebehaviorofscientistsandmathematicianscontainsanumberofdescriptivestudiesofcognitivemobility(seeWagnerDobler,1999;Basu,2011;andBasuandWagnerDobler,2012).Thesestudiesusemigrationamongthefieldsofmathematicstodeterminewhichfieldsare“closer”toeachotherandtoexaminetheformationofnetworks.Inrelatedwork,Galenson(2005)andGalensonandWeinberg(2000)provideafascinatinganalysisofthechangingcreativityofartistsoverthelifecycle.

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setofquestionsmayrespondtosupplyanddemandshocksbyshiftingtheir“mental

powers”andotherresourcestoadifferentsetofquestions.Cognitivemobilitythus

measuresthetransitionfromonelocationtoanotherinideaspace.

Anumberofrecentstudiesdocumentthattheentryorexitofhigh‐skillresearchers

mayinfluencetheproductivityofthoseworkerswhoarecreativelyclosetothem(see

Azoulay,ZivinandWang,2010;andWaldinger,2010)atleastasmuchasitinfluencesthe

productivityofnativeswhoaregeographicallyclose(seeWaldinger,2012).2Thisfinding

suggeststhatthecostsandbenefitsoftheimmigrationofknowledgeproducerscannotbe

evaluatedwithoutdocumentingwhethernativeschangethetypeofcreativeworkthatthey

engageinasaresponse.Thisisadifficultquestionthathasnotyetbeenaddressedbythe

literature,mainlybecauseansweringitrequiresdeterminingtheintellectualcontentof

individualresearchers'contributionsovertime.

Inthispaper,weexaminehownativesreallocatethemselvesinideaspaceasa

resultofasupplyshockthatgreatlyincreasedthenumberofknowledgeproducers

workingonspecifictopics.3Inparticular,weexaminethecognitivemobilityofAmerican

mathematicianstriggeredbytheinfluxofSovietmathematiciansafterthecollapseofthe

SovietUnionintheearly1990s.Nearly10percentoftheSovietmathematicalworkforce

leftthecountryafteritspolitical(andeconomic)unraveling,withadisproportionate

numbersettlingintheUnitedStates.

2SeealsoFurman,Kyle,Cockburn,andHenderson(2005);HuntandGauthier‐Loiselle(2010);Kerr

andLincoln(2010);andMoser,Voena,andWaldinger(2012).

3Cognitivemobilityflows,ofcourse,canalsoresultfromdemandshocks.Asimpleanecdotalexamplewillsuffice:Thestudyofthe“GreatModeration”seemstohavebeenanimportanttopicinmacroeconomicsbetween2000and2008.However,thefinancialcrisisof2008andthesubsequentsevererecessionlikelymotivatedmanyofthemacroeconomistsstudyingthepresumedtamingofthebusinesscycletofindmorefertile(andmarketable)areasofresearch.

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InBorjasandDoran(2012),weexploitedtheunexpectedcollapseoftheSoviet

Unionandtheunbalancednatureoftheensuingsupplyshocktoshowthattheincreased

numberofmathematiciansintheUnitedStatesledtoasignificantdeclineinthevolumeof

scientificoutputproducedbycompetingAmericanmathematicians.4Wenowexaminethe

repercussionsofthesupplyshockonthelocationalchoicesofAmericanmathematiciansin

ideaspace.

Standardmodelsofknowledgeproductionsuggestthatthesupplyresponsecanbe

eitherpositiveornegative,dependingonwhetherspillovereffectsresultingfromthe

increaseinthesizeofthestockofideasorthescarcityconstraintsimpliedbythelawof

diminishingreturnsdominate.Asaresult,thedirectionofflowsofcognitivemovers

providesindependentinformationabouttherelativeimportanceofhumancapital

spilloversintheknowledgeproductionsector.Mostimportant,inaworldwherethe"true"

productivityofknowledgeproducersishardtomeasure,examiningcognitiveflowsallows

ustobypassthemeasurementproblems.Aspeople“votewiththeirminds,”theyshare

privateinformationaboutrelativeproductivitiesindifferentlocationsofideaspacethat

countsofpublications,patents,andcitationsmaymiss.

OurdataconsistofacompletetabulationofallpublicationsbyAmerican

mathematiciansbetween1940and2009,includingdetailedinformationonthe“field”of

eachpublication.5Thesedataallowsustoexaminetheevolutionofresearchtopicsand

interestsoveraparticularmathematician’sworkinglife.Wefindthatthesupplyshock

4AbramitzkyandSin(2012)examinethecodifiedknowledgeflows(asmeasuredbybook

translations)resultingfromthisshock.Ganguli(2013)examineshowSovietscientificresearchwasusedintheWestbeforeandaftertheshock.

5Dubois,Rochet,andSchlenker(2012)useasubsetofthisdatatoexaminethecorrelatesofthegeographicmobilityofmathematicians.

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generatedastrongcognitivemobilityresponse:pre‐existingAmericanmathematicians

relocatedwithinideaspacetoresearchtopicsandquestionsthatdidnotreceivealarge

numberofSovietémigrés.WealsodocumentthatnewentrantstotheAmerican

mathematicscommunitybegantosystematicallyavoidSoviet‐styletopicsoverthetwo‐

decadeperiodaftertheSovietinflux.

Ouranalysisidentifiescoststhatarecorrelatedwithcognitivemobility,andshows

thattheSovietinfluxincreasedthosecostsforasignificantnumberofAmerican

mathematicians.Inparticular,thedatarevealthatmathematicianswhomovetoadifferent

pointinideaspacetakelongertoproducetheirnextpaperthanmathematicianswhostay

withintheircomfortzoneandcontinueworkinginfieldswheretheyhavepriorexperience.

InadditiontothefindingthattheSovietinfluxincreasedthenumberofcognitivemovers

(andhenceincreasedthelengthoftheaverage“preparationspell”forthenextpaper),we

alsodocumentthatthelengthofthepreparationspellitselfincreasedsignificantlyfor

thoseAmericanmathematicianswhoexperiencedthestiffestcompetitionfromtheSoviet

émigrés.Thisevidenceisconsistentwiththepresenceofcongestioncosts,asmany

mathematicianswhoworkinonenarrowareatrytomoveatoncetoanotherarea.

Finally,ourdataallowsustoexaminesomeofthedeterminantsofcognitive

mobility.Inparticular,wefindthatexperienced(andlikelytenured)andhigh‐ability

mathematicianswererelativelylesslikelytoswitchfieldsthanweretheyoungerorless

productivemathematicians.Thisimpliesthateitherthecostsofcognitivemobilitywere

higherforthebestmathematicians,orthatthenetbenefitsfromhumancapitalspillovers

werehigher.Giventhatthe“excess”publicationlagassociatedwithpost‐1992cognitive

mobilityislowerforhigh‐abilitymathematicians,theevidenceismostconsistentwiththe

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conjecturethatthebeneficialspillovereffectsresultingfromtheinfluxofhighlyskilled

SovietmathematiciansaccruedmainlytothemostproductiveAmericanmathematicians.

II. Conceptual Framework

Ourbasicmodelofknowledgeproductionisinspiredbymoderntheoriesof

economicgrowththatemphasizehowhumancapitalexternalitiesaffecttheproductivityof

specificworkers(JonesandRomer,2012).Aworkersurroundedbyahigh‐skillworkforce

mayhimselfbecomemoreproductivethroughexposuretonewideasandconcepts.Itis

wellknown,however,thatthesespillovereffectsmustcoexistwiththetraditionallawsof

scarcityanddiminishingreturnsthatformthecoreofeconomicanalysis.

Considerthesimplestmodelwheretheproductionfunctionfor“mathematical

knowledge”intheUnitedStates,Y,dependsonthestockofideasI,thestockofcapitalK

usedasinputs(e.g.,facultyslotsandcomputingresources),andthestockof

mathematiciansL.SupposethereareconstantreturnstoKandLandthattheproduction

functionisgivenby:

(1) Y I K L1 ,

wheregivesthe“externalitieselasticity.”Aslongasthestockofideasisproportionalto

thesizeoftheworkforce,itiseasytoshowthattheshort‐andlong‐runeffectsofasupply

shock(m=dlogL)onthemarginalproductofmathematiciansis:

(2) d log MPL

()m, if d log K 0

m, if d log K m.

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Thesignoftheshort‐runeffectdependsontherelativestrengthofthespilloverselasticity

andthetraditionalcompetitiveeffect.Overtime,however,thecapitalstockadjuststothe

supplyshock.Ifspillovereffectsexist,thelong‐runimpactwillbepositivebecausethe

stockofideasexpanded,increasingworkerproductivity.

Tointroducethenotionofcognitivemobility,weallowforthepossibilitythatthe

mathematicsworkforceisnothomogenous.Mathematics,likeallotherdisciplines,is

composedofdistinct“fields.”Theexternalitycapturedbyisaglobalhumancapital

externality:thechangeinthetotalstockofmathematicalideasshiftstheproductivityofall

mathematiciansbythesameproportion.However,asupplyshockthatdifferentiallyaffects

thesizeoftheworkforcein,say,GeometricTopologyandQuantumTheorymighthave

differentimpactsonthestockofideasusefultoresearchersinthosetwoareas.

Thesimplestwaytoincorporatetheexistenceofdifferentmathematicalfieldsisto

reinterpretthevariableLasthenumberofefficiencyunitssuppliedbythemathematics

workforce.6SupposethereareFdistinctmathematicalfieldsanddefinethetotalnumberof

efficiencyunitsas:

(3) L I1L1

... IFLF

1/,

whereIfgivesthestockofideasinfieldf;Lfgivesthesizeoftheworkforceinthatfield;is

thelocalexternalityelasticitymeasuringthesizeoffield‐specificspillovers;andthe

elasticityofsubstitutionbetweenmathematiciansindifferentfieldsis=1/(1‐).

6SeeBorjasandDoran(2013b)foranextendeddiscussionofthemulti‐levelCESframeworkinthe

humancapitalexternalitiescontext.

8

Forsimplicity,supposewecancategorizeallresearchinmathematicsasSoviet‐

styleresearch(S)orAmerican‐styleresearch(A).LetmSandmAgivethepercentchangein

thenumberofSoviet‐styleandAmerican‐stylemathematiciansresultingfromthesupply

shockfollowingthecollapseoftheSovietUnion,withmS>mA.Theimpactofthesupply

shockontherelativeproductivityofmathematiciansworkinginthesetwoareasisthen

givenby:7

(4) d log MPS d log MPA 1

(mS mA ),

inboththeshortandlongruns.Notethattheglobalexternalitydoesnotaffectthechange

intherelativemarginalproductsinceitexpandstheproductivityofallmathematicians

equally,regardlessoffield.Further,thedistributionalimpactsummarizedby(4)persistsin

thelongrun,evenafterthecapitalstockhasadjusted.Finally,thenetimpactofthesupply

shockcanbepositiveornegative,dependingonwhetherthelocalexternalityelasticityis

largerthanthecompetitiveeffectmeasuredbytheinverseoftheelasticityofsubstitution.

Regardlessofthedirectionoftheneteffectinequation(4),thesupplyshockmay

triggerasupplyresponse.8Thesignofthenetproductivityimpactmayinduceaninflowof

mathematiciansfromotherfieldsintotheSoviet‐dominatedfields(iftheneteffectis

positive),oranoutflowofmathematicianscurrentlyconductingresearchintheSoviet‐

7Thederivationofequation(4)assumesthatthestockofideasinaparticularfieldisproportionalto

thenumberofworkersinthatfield.

8Anumberofrelatedstudiesexaminehowimmigrationaffectsthehumancapitalinvestmentdecisionsofnativeworkers.Llull(2010)estimatesastructuralmodeloftheU.S.labormarket,concludingthatnativesadjustedtheirhumancapitalandlaborsupplybehaviorinresponsetoimmigration,whileHunt(2012)measuresnativehumancapitalresponsestoimmigrationusingapaneldatasetofU.S.states.

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dominatedfieldsintothosefieldslessaffectedbythesupplyshock(iftheneteffectis

negative).9

Itiseasytodescribethemechanismgeneratingthesecognitivemobilityflows.Let

MPiSandMPiAdenotethemarginalproductofmathematicianiintheSoviet‐andAmerican‐

stylefields,respectively.Anincome‐maximizingmathematicianwhodecidedtoconduct

researchinSoviet‐dominatedfieldspriortothecollapseoftheSovietUnionmusthave

satisfiedtheinequalityMPiS>MPiA.Letimeasuretheneteffectofthesupplyshockonthe

productivityofmathematiciani.Afterthesupplyshock,aSoviet‐stylemathematicianwill

engageincognitivemobilityandbegintoconductAmerican‐styleresearchonlyif:

(5) MPiS+i<MPiA–Ci,

whereCigivesthecostsofcognitivemobility(e.g.,retoolingskills,investinginanew

networkofcollaborators,movingtoanewinstitution,etc.).Weassumethatthesemobility

costsarestrictlypositive.

Thepre‐shockrevealedpreferenceofmathematicianiimpliesthataSoviet‐style

mathematicianwillswitchtoAmerican‐styleresearchifandonlyif:

(6) i<–Ci.

Sincemobilitycostsarepositive,aSoviet‐stylemathematicianrespondstothesupply

shockbyswitchingtoAmerican‐styleresearchonlyiftheneteffectiisstronglynegative.

Putdifferently,ifweweretoobservemanySoviet‐stylemathematiciansswitchingto

9Notethatthesupplyresponseinthespaceofideasisnotidenticaltoasupplyresponseinthespace

ofoccupations.Aresearchprofessormayremainaresearchprofessor,atthesameinstitution,withthesamejobtitle,institutionalcolleagues,paystructure,andresponsibilities,whiledrasticallyrefocusinghismentaleffortsonadifferentsetofresearchquestions.

10

American‐styletopicsintheaftermathofthesupplyshock,thisobservationnecessarily

impliesthattheadversecompetitiveaffectsarisingfromthesupplyshockmustbefar

strongerthanthepositivespilloversgeneratedbytheexpansioninthestockofideas.

Similarly,considerthecognitivemobilitydecisionofmathematicianswhoare

conductingAmerican‐styleresearchpriortothesupplyshock.Thissubsampleof

mathematiciansmustsatisfytheinequalityMPiA>MPiS.Mathematiciansinthisgroupwill

switchtoSoviet‐styleresearchafterthesupplyshockif:

(7) MPiS+i–Ci>MPiA.

BecausethesemathematicianshadaninitialadvantageinconductingAmerican‐style

research,theobservationofcognitivemobilitytoSoviet‐stylefieldsimpliesthat:

(8) i>Ci.

Inotherwords,cognitivemobilityfromAmerican‐styletoSoviet‐styleresearchimpliesthe

presenceofstrongpositiveexternalities.

Itisimportanttoemphasizethatcognitivemobilitywillbeobservedonlyifthenet

spilloverisnumericallylargeregardlessofsign.Thenetspilloverwillbestronglypositiveif

thecognitivemoversaremainlycomposedofmathematiciansswitchingfromAmerican‐to

Soviet‐styleresearch;oritwillbestronglynegativeifthemoversflowintheopposite

direction.Regardlessofthesignofi,thenetspillovermustoutweighthecostsofcognitive

mobility.Weshowbelowthatthesecostsaresizableandlikelyincreasedafterthesupply

shock.10

10Itiseasytoexpandthemodeltolearnmoreabouttheselectionthatcharacterizesthesampleof

cognitivemovers.Afterall,thereisprobablyagreatdealofheterogeneityinthemagnitudeofthenet

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III. Historical Context and Data

Ourempiricalexplorationoftheconceptandrelevanceofcognitivemobility

examinestheresearchdecisionsmadebymathematiciansintheUnitedStatespriortoand

afterthecollapseoftheSovietUnion.AsdocumentedbyBorjasandDoran(2012),aftera

longperiodofinfrequentcontactsbetweenSovietandWesternmathematicians,over1,000

Sovietmathematicians(orroughly10percentofthestock)lefttheSovietUnionafter1992,

witharoundathirdeventuallysettlingintheUnitedStates.Thisparticularhistoricalevent

hasanumberofkeyfeaturesthatplayacrucialroleinouridentificationstrategy:

(1)TheopportunityforlargenumbersofSovietmathematicianstomigratetothe

UnitedStatesaroseunexpectedlyandsuddenly,beginningaroundthetwo‐yearperiod

surroundingthecollapseofSovietcommunismin1990‐1991.

(2)Thesupplyshockwaslarge,bothbecauseofthelatentdemandforimmigration

afterdecadesoftightlysealedbordersandbecauseofthesuddencollapseoftheSoviet

economy(Ganguli,2010).11

(3)NeitherSovietnorAmericanmathematiciansanticipatedtheabruptopeningof

bordersduetotheliftingoftheIronCurtain,sothatdecisionsmadepriorto1992to

specializeinspecificareascanbeviewedasexogenous.

spillover(i)andmigrationcosts(Ci)acrossmathematicians.Theselectionrulethatdeterminesthesubsampleofmoverswilldependonthecorrelationbetweenthesevariablesandamathematician’sinnateability.Weprovideevidencebelowsuggestingthathigh‐abilitymathematicianslikelybenefitedthemostfromthehumancapitalspillovers.

11EventhoughtheSovietémigréswhomovedtotheUnitedStatesincreasedthenumberofmathematiciansinthecountrybyonly1.1percent,theirpre‐1992outputasdefinedbythenumberofpaperspublishedwasequalto3.4percentoftheoutputofAmericanmathematicians.GroggerandHanson(2013)documentthatthesampleofscientificimmigrantstotheUnitedStatesconsistsofpersonsofhighacademicability.

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(4)TheSovietmathematicalcommunitywasnotasbroadasitsAmerican

counterpart;further,itexcelledinspecificareasduetopath‐dependenceinSoviet

mathematicalinsightsandtherelativelyinfrequentcontactbetweenSovietandWestern

mathematiciansduringthedecadesofSovietcommunistrule.

(5)ThesupplyshockresultingfromthecollapseoftheSovietUnionwas

“unbalanced”inthatitincreasedthesupplyofAmericanmathematiciansworkingin

differentfieldsdifferentially;someAmericanmathematicianswerehighly“exposed”tothe

Sovietinflux,whileotherAmericanmathematiciansbarelynoticedtheripplesofthe

shock.12

Asaresult,thepost‐1992influxofSovietmathematiciansintotheUnitedStates

providesauniqueopportunitytoobservehownativeknowledgeproducersrespondto

newtalentthatsuddenlychoosestolocateclosetotheminthespaceofideas.Around1992,

someAmericanmathematiciansfacedaninfluxofnewcolleaguesandcompetitorsintheir

specificresearchareas,whileotherAmericanmathematiciansdidnot.Ourempirical

strategyistocomparethedegreeofcognitivemobilityexperiencedbythesetwogroupsof

Americanmathematiciansbothbeforeandaftertheshock.

ItisimportanttoemphasizethatalthoughthefielddistributionofactualSoviet

émigréstotheUnitedStateswasselectedinpartduetoAmericandemandforspecific

typesofmathematiciansatthattime,thehistoricalcontextsuggeststhatthedistributionof

allSovietmathematiciansacrossfieldsbefore1992wasnotrelatedtoU.S.demand.Thus,a

12Inadditiontoincreasingthequality‐adjustednumberofpre‐existingAmericanmathematicians,

theSovietémigréscontinuedtospecializeinSoviet‐stylefieldsafterarrivingintheUnitedStates.SovietémigrésintheUnitedStatespublished47percentoftheirpre‐1992papersand41percentoftheirpost‐migrationpapersinthe1990sinSoviet‐stylefields(asdefinedbelow).Incontrast,pre‐existingAmericanmathematicianspublishedonly31percentoftheirpost‐1992papersinSoviet‐stylefields.

13

keyfeatureoftheempiricalstrategyisitsuseofthepotentialsupplyshockacrossareasof

knowledge,measuredbythepre‐1992Sovietdistributionofmathematiciansacrossthe

fieldsofmathematics.

Themostcomprehensivedataavailableonthepublishedcontributionsofindividual

mathematicians(bothintheUnitedStatesandabroad)iscontainedintheAmerican

MathematicalSociety’s(AMS)MathSciNetarchives.TheAMSgaveusaccesstothe

informationinthisarchiveandprovideduswithadatabasethatreportsthenumberof

paperspublishedbyeverymathematicianintheworld,byfieldandyear,since1939.In

additiontotheinformationonthenumberofpapers,theAMSdatareportsthe

mathematician’sinstitutionalaffiliationatthetimethepaperwaspublished,aswellasthe

locationoftheaffiliation.TheAMS,however,onlybegantocollecttheaffiliation

informationonasystematicbasisaround1984,sothataffiliationandlocationarenot

typicallyavailableforearlierpapers.Mostimportant,theAMSprofessionalstaffassigns

eachpublicationinmathematicstooneofthemanyfieldsthatmakeupthestudyof

mathematics.TheAMSprovideduswiththeauthor‐year‐fieldinformationatthetwo‐digit

fieldlevel,classifyingeverypublicationbyeachmathematicianoverthe1939‐2009period

intooneof73differentfields.13

BorjasandDoran(2012)usedthesedata,mergedwithinformationfromthe

ThomsonReuters’InstituteforScientificInformation(ISI)WebofSciencearchiveanddata

fromtheMathematicalGenealogyProject(MGP),toconstructtheuniverseofactive

AmericanmathematicianspriortothecollapseoftheSovietUnion.Ingeneralterms,Borjas

13Inourearlierwork(BorjasandDoran,2012),wespecificallyusedthepublicationhistoryof

Americanmathematiciansbetween1978and1989asthe“baseline.”Only63ofthesubjectsarepopulatedduringthatperiod.

14

andDoran(2012)definedthepopulationofactiveAmericanmathematiciansascomposed

ofpersonswho,priorto1989,hadpublishedpredominantlyusinganAmericanaffiliation,

orwho,intheabsenceofanyaffiliationdata,obtainedtheirdoctoraldegreefroman

Americaninstitution.

TheempiricalanalysisreportedbelowalsousesthesampleofAmerican

mathematicianswhofirstenteredresearchactivityafter1990.Weapplythedefinitions

introducedinBorjasandDoran(2012)toconstructthemorerecentcohortsofAmerican

mathematicians.Inparticular,weexaminethelocationoftheaffiliationsreportedinthe

paperspublishedinthefirstfiveyearsofamathematician’scareer,andclassifytheperson

as“American”ifmorethanhalfofthosepublicationsusedanAmericanaffiliation.14

Weconstructapanelwhereanobservationrepresentsamathematician/paper

permutation.Foreachmathematician/paper,weknowboththepaper’stwo‐digitfield

codeandtheyearofpublication.Inshort,ourdatadescribestheentirepublicationhistory

ofAmericanmathematiciansbetween1940and2009.Table1reportssomesummary

statisticsofthedataset.Itcontainsatotalof711,497publishedpaperswrittenby78,684

uniqueAmericanmathematicians,andabout44percentofthesemathematiciansentered

activeresearchactivitybefore1992.

Wewishtoexaminethetrendsinthefielddistributionofpaperspublishedby

Americanmathematicians.Table2illustratesthedramaticdifferencesinspecializations

betweenSovietandAmericanmathematicspriortothecollapseoftheSovietUnion.In

particular,thetablereportsthe“topten”fieldsintheSovietUnionbetween1984and1989,

14TheDataAppendixintheextendedworkingpaperversionofthispaper(BorjasandDoran,

2013a)containsadetaileddescriptionofthedataandtheconstructionofthesamples.

15

rankedbytheshareofSovietpapersinthatfield.ThetoptwoSovietfieldsarePartialand

OrdinaryDifferentialEquations,andthesetwofieldsaccountforalmost18percentofall

Sovietpublications.Incontrast,onlyabout5percentofAmericanpaperswrittenduring

theperiodwereinthosetwofields.Moregenerally,thetopfivefieldslistedinTable2

accountfor35.6percentofallSovietpublications,butonlyabout19.1percentofAmerican

publications,whilethetoptenfieldsaccountfor53.2percentofallSovietpublicationsand

36.5percentofAmericanpublications.

Toreducethedimensionalityoffieldchoicefromthe73potentialoutcomes,we

initiallyconstructasimpleindexindicatingthe“Soviet‐ness”ofaparticular

mathematician’sresearchinterestsatapointintime.Inparticular,foreachpaperwritten

byanAmericanmathematician,wecreateadummyvariableindicatingifthepaperisina

“Soviet‐stylefield”—i.e.,thepaperisinoneofthetenfieldslistedinTable2.15Aswillbe

shownbelow,wereplicatedouranalysisusinganumberofalternativedefinitionsof

Soviet‐stylefields,aswellasmeasuresof“cognitivedistance”fromtheSovietresearch

agenda,andfindthattheresultsarerobusttotheuseofalternativeclassifications.

Table1alsoreportssummarystatisticsforthefractionofSoviet‐stylepapers

writtenbyAmericanmathematicians.ThedatashowthatthefractionofSoviet‐style

15Dependingonthecontentofthepaper,MathSciNetprovidesdetailedinformationnotonlyonthe

primaryfieldclassification,butalsoonsecondary,tertiary(andevenlower‐level)fieldclassifications.AlthoughthedatabasethatAMSprovidedtousonlycontainstheprimaryfieldcategory,weareabletodeterminethesecondary,tertiary,quaternary,andquintinaryfields(iftheyexistinthefirstplace)foranon‐randomsampleof50percentofthepre‐1992papersintheAMSdatabase.WefindthatathirdoftheSoviet‐stylepapersreportasub‐primaryfieldthatisnotSoviet‐style.Butmanyofthesefieldsarefardowninthelist:onlyoneoutofeveryfourSoviet‐stylepapersreportsasecondaryfieldthatisnotaSoviet‐stylefield.Ifweassumethatapaper's"true"fieldisaweightedaverageofthemultiplefieldclassifications,withtheprimaryfieldweightedtwiceasmuchasthesecondaryfield,whichisweightedtwiceasmuchasthetertiaryfield,etc.,thentheaveragepaperinourSoviet‐stylecategoryhasa"true"fieldindexthatis89.2percentSoviet‐style,andtheaveragepaperintheAmerican‐stylecategoryhasa"true"fieldindexthatis1.6percentSoviet‐style.Evenwithvariationsinourweightingscheme,itisclearthatoursimpleclassificationcapturesthepredominantfieldcontentofthesepapers.

16

paperswrittenbythepre‐existinggroupofAmericanmathematiciansdeclinedfrom33.4

percentforpaperspublishedbefore1992to31.6percentforpaperspublishedafter1992.

Newentrantsintothemathematicsmarketalsobecamelesslikelytowritepapersin

Soviet‐stylefields.Inparticular,thetablereportstheprobabilitythatthefirstpaper

publishedbyamathematicianinhiscareer,whichwewillcallthe“dissertation”paper,isin

aSoviet‐styletopic.Thetrendsarerevealing:32.0percentofdissertationswrittenpriorto

1992wereinSoviet‐styletopics,ascomparedtoonly25.1percentofdissertationswritten

after1992.

IV. The Determinants of Cognitive Mobility

Supposethateachofthedistinctfieldsofmathematics(e.g.,StatisticsorNumerical

Analysis)representsaspecificlocationinthespaceofideas.Whilewritingapaperinone

ofthesefields,amathematicianresidesinthatlocationinideaspace.Afterthe

mathematiciancompletesaparticularpaper,hebeginsa“preparationspell”thatends

whenthesubsequentpaperispublished.

Duringthepreparationspell,amathematicianconsidersthebenefitsandcostsof

stayingintheparticularresearcharea.Thiscalculationmaymotivatethemathematicianto

remaininthesamelocationinideaspace,ortochooseanewlocation.Asupplyshockof

newmathematiciansintoasubsetoflocationsinideaspacealtersthecost‐benefitcalculus.

Citationratesinmathematicsarefarhigherwithineachfieldthanacrossfields.16Asa

result,theincreaseinthestockofknowledgeataparticularlocationinideaspaceresulting

16Forexample,80percentofthecitationsinthepaperspublishedinthetop10Soviet‐stylefields

aretopapersinthosesame10fields;seealsoBorjasandDoran(2012),p.1169.

17

fromthesupplyshockcouldincreaseproductivityformathematiciansalreadyresidingin

thatlocation.Butthesupplyshockmayalsoincreasethecostsofstayinginthatlocation:

moremathematiciansnowcompeteforresourcesandattentioninthatfield.Equally

important,themathematicianrecognizesthatcognitivemobilityiscostly:thedurationof

thepreparationspellmaybelongerifhemustlearnanewsetofskillsandmathematical

techniqueswhenmovingtoadifferentpointinideaspace.

Thissectionexaminestworelatedquestions.First,whichfactorsinducea

mathematiciantomovetoadifferentlocationinideaspaceinresponsetoasupplyshock?

Second,doesthecognitivemobilityrepresentamovementtowardstheresearchquestions

favoredbynewcomersorawayfromthem?AsthemodelpresentedinSectionIIshowed,

thenetchangeintherelativemarginalproductthatamathematicianfacesintwopotential

locationsinideaspacedependsontherelativestrengthsof(local)humancapitalspillovers

andtheincreasedcompetitionimpliedbythelawofdiminishingreturns.Thedirectionof

cognitivemobilityflowsprovidesinformationaboutwhichofthesetwoeffectsisdominant.

Webegintoaddressthesequestionsbyexaminingthelocationalchoicesinidea

spaceforthegroupofAmericanmathematicianswhoenteredactiveresearchactivityprior

to1992.Wedefinetwodistinctgroupsofpre‐existingAmericanmathematicians:those

whosepre‐1992dissertationwasonaSoviet‐styletopic,andthosewhosepre‐1992

dissertationwasnot.17Thissimpleapproachexploitsthefactthatthepre‐existing

17Throughouttheanalysis,weusetheterm“dissertation”torefertothefirstpaperpublishedina

mathematician’scareer.Althoughthisisaconvenientexpositionaldevice,wesuspectthatinmostcasesthesubjectofamathematician’sfirstpaperisindeedthesubjectoftheactualdoctoraldissertation.WeusethedissertationpapertodefinethegroupsofSoviet‐andAmerican‐stylemathematiciansfortwodistinctreasons.First,thedissertationtopicreflectsthetrainingacquiredoveramulti‐yearperiodthatpresumablypreparedthemathematicianfortheresearchconcernsheintendedtopursueafterthedoctorate.Moreimportantly,wedefinetheextentofcognitivemobilitybyobservingthefieldofeachpaper(afterthedissertationpaper)publishedoverthemathematician’scareer.Inordertoavoidselectingonthedependentvariable,wemust

18

mathematicianschosetheirdissertationtopicswithoutconsideringanypotentialcostsor

benefitsarisingfromfuturecompetitionorcollaborationwithSovietmathematicians.

Thechallengeinempiricallymeasuringcognitivemobilityisthatmathematicians

sometimesalternatethetopicsthattheyworkonfrompapertopaper.Weneedameasure

ofcognitivemobilitythatdoesnotinterpretaregularvacillationbetweenField#7and

Field#32onasetofconsecutivepapersasasetoffast‐pacedcreativejourneysbetween

thesesubjects;itismorelikelythatthisvacillationitselfrepresentsthemathematician’s

constant“location”inthespaceofideas.

Weinitiallyconsidertwoconceptuallydistinctwaystomeasureachangeinlocation

inthespaceofideas.First,wecanobservewhethereachofthemathematician’sfuture

papersisinthesameareaasthedissertationtopic,andmeasurehowtheprobabilityof

writinginone'sdissertationareachangesovertime—andparticularlyhowitchangesafter

theSovietsupplyshock.Thisapproachisakintothinkingofamathematician’s"location"in

thespaceofideasastheprobabilitydistributionofthatmathematician’soutputacross

fields.Forsimplicity,wereducethedimensionalityofthemeasurementbydividingfields

intotwocategories(Soviet‐andAmerican‐style).Wefurthersimplifythemeasurement

problembymeasuringallchangesrelativetothefieldofthedissertationpaper.

Alternatively,wecandefinecognitivemobilitybyobservingthefirsttimethata

mathematicianpublishesinaspecificfield.Wecanmeasuretheprobabilitythat

mathematicianswriteforthefirsttimeinanewareawheretheyhaveneverworkedin

before,andagainobservehowthisprobabilityevolvesovertime.Thismeasureofcognitive

excludefromourregressionsanypapersusedtodefineoursubgroups.Thedefinitionofthesubgroupsaccordingtothefieldofthefirstpublishedpaperallowsourregressionstoexcludeasfewpapersaspossible.Ourresultsarerobusttousingadditionalpapers(e.g.,paperspublishedinthefirst2or5years)todefinethesubgroupsofmathematicians.

19

mobilityisobviouslynotidenticaltothemeasuredefinedinthepreviousparagraph;even

ifthedistributionofpapersacrosssubjectsdoesnotchangeappreciably,thetendencyto

exploreabrand‐newareamay(ormaynot)changeagreatdealovertime.

Asnotedabove,wereducethedimensionalityoflocationsinideaspaceby

compressingthe73fieldsofmathematicsintotwocategories:(1)Soviet‐stylefields,

composedofthe10fieldsthatwerethemostpopulatedintheSovietUnionpriortothe

collapse;and(2)American‐stylefields,theresidualgroupofthe63otherfields.18

Usingthissimpletwo‐wayclassification,weplotourfirstmeasureofcognitive

mobility,theprobabilitythatapaperwritteninyeartisinadifferentfieldthanthe

dissertation,inthetoppanelofFigure1.Inthe1980s,beforethecollapseoftheSoviet

Union,AmericanmathematicianswhowrotetheirdissertationsonAmerican‐styletopics

hadanaverageprobabilityofabout20percentofwritinginaSoviet‐stylefieldinlater

papers.ThisprobabilityremainedroughlyconstantaftertheSovietinflux;infact,if

anything,thereisaslightdeclineafter1992.Theevidencethussuggeststhatthesupply

shockeitherhadnoimpactorasmallnegativeimpactonthepropensityforcognitive

mobilityamongmathematicianswhobegantheircareerinAmerican‐stylefields.Interms

ofthemodel,itseemsthatthemobilitycostsoflocatinginadifferentpointinideaspace

forAmerican‐stylemathematiciansfarexceedany(potential)positivespillovereffects.

Incontrast,beforethecollapseoftheSovietUnion,Americanmathematicianswho

wrotetheirdissertationsonSoviet‐styletopicshada30to35percentprobabilityof

writingonanon‐Soviettopicineachoftheirlaterpapers.Butthisprobabilitybeganto

18Thisreductionindimensionalityimpliesthatthe“brandnewfield”measureofcognitivemobility

identifiesthefirsttimethatamathematicianwithaSoviet‐style(American‐style)dissertationswitchedtoAmerican‐style(Soviet‐style)research.

20

increaserapidlyaftertheSovietinflux,reachingapeakofabout50percentby2005.The

datathussuggeststhatthesupplyshocksubstantiallyincreasedthepropensityfor

cognitivemobilityamongAmericanmathematicianswhowroteaSoviet‐styledissertation.

Putdifferently,thedatarevealthatAmericanmathematicianswhostartedtheircareersin

alocationinideaspacethatreceivedalargenumberofSovietémigrésrespondedtothe

influxbymovingtoanewlocationthatreceivedfewerimmigrants.Intermsofthemodel,

thedirectionoftheflowofcognitivemoversimpliesthatthenetspillovereffectmustbe

stronglynegativesinceitmustoutweighthemobilitycosts.

PanelBofFigure1illustratesthetrendsusingoursecondmeasureofcognitive

mobility,ameasurethatindicateswhetheramathematicianentereda“brandnew”fieldin

yeart(i.e.,afieldwherehehadneverpublishedbefore).Thefigureclearlyshowsthat,

withinafewyearsafterthestartoftheSovietinflux,therewasasharpincreaseinthe

tendencyofSoviet‐stylemathematicianstoexploreother(i.e.,non‐Soviet)researchareas

forthefirsttime.Notethattheincreaseintherateofcognitivemobilityisobservedaround

fiveyearsafterthesupplyshock.Aswewillshowinthenextsection,thistimingroughly

coincideswiththeamountoftimerequiredtoretoolmathematicalskillsfromAmerican‐

styletoSoviet‐stylefields.Inshort,bothpanelsofFigure1demonstratealargeincreasein

therateofcognitivemobility,howeveritismeasured,forSoviet‐stylemathematiciansafter

theinfluxofSovietémigrés.

Toexaminethesensitivityofourfindingstocontrollingforvariousbackground

characteristics,weestimatedthelinearprobabilityregressionmodel:

(9) pin(t)=i+t+(Ti×Si)+Zi+,

21

wherepin(t)istheprobabilityofcognitivemobilityfromthedissertationtopapern

publishedbymathematicianiincalendaryeart;Tisadummyvariableindicatingifthat

paperwaspublishedafter1992;Siisadummyvariableindicatingifthemathematician’s

dissertationtopicwasinaSoviet‐stylefield;Zisasetofcharacteristicsthatmayinfluencea

mathematician’slocationinideaspace(discussedbelow);andiandtarevectorsof

individualandcalendaryearfixedeffects,respectively.Itisimportanttoemphasizethat

thisregressionmodelisestimatedusingonlythesampleofpre‐existingAmerican

mathematicians.19

Table3reportstherelevantcoefficientsfromthisregressionmodelusingseveral

alternativespecifications.Regardlessofthespecification,wefindthatthesupplyshockled

toasubstantialincreaseincognitivemobilityoutofSoviet‐styleareasandintoAmerican‐

stylework.Consider,forinstance,thesimplestspecificationreportedincolumn1,which

onlyincludesamathematician’syearsofexperience(introducedasaquartic)inthevector

Z.Thecoefficientoftheinteractionvariablebetweenthepost‐1992indicatorandthe

variableindicatingwhetherthemathematicianwroteaSoviet‐styledissertationis

around.12,regardlessofthemeasureofcognitivemobilityused.Putdifferently,the

(relative)probabilityofmovingtoAmerican‐styleresearchforSoviet‐stylemathematicians

increasedbyabout12percentagepointsafterthesupplyshock.20

19Theregressionsthatusethemeasureofcognitivemobilitytoa“brandnewfield”asadependent

variableonlyincludethosespellsthatpotentiallyallowforsuchamoveoccur.OnceaSoviet‐style(American‐style)mathematicianwriteshisfirst‐everAmerican‐style(Soviet‐style)paper,allsubsequentspellsinthatmathematician’scareermusthaveazeroforthedependentvariable.Weexcludeallthosesubsequentspellsfromtheregressions.

20Webrieflynotetwodistinctrobustnesschecks.First,althoughthestandarderrorsreportedinthetablesadjustforindividual‐levelheteroscedasticity,theresultsremainstatisticallysignificantifweclusterthestandarderrorsatthebroaderdissertation‐fieldlevel.Second,foursubjectswereaddedduringtherevisionoftheMathematicsSubjectClassificationin2000.Ourresults,however,arenotaffectedbythis

22

Thedataalsoallowsustoexaminethequestionofwhichmathematiciansaremost

likelytoengageincognitivemobility.Asourmodelshowed,cognitivemobilityoccurs

whenthenetspilloversduetoaninfluxofmathematiciansintoaparticularlocationinidea

spaceoutweighthecostsofmigration.Asaresult,thecognitivemoversareaself‐selected

groupofmathematicians.Hence,wecanexaminethedistinctivecharacteristicsofthis

grouptolearnabouthowthenetspilloversorthemobilitycostsdifferamongdifferent

mathematicians.

ThesecondcolumnofthetableincludestwoadditionalvariablesinthevectorZ:an

indicatorofwhetherthemathematicianwaslikelytobetenuredasof1992,andthe

mathematician’srateofoutput,asmeasuredbythenumberofpapersthatthe

mathematicianpublishedannuallypriorto1992.21Theindividualfixedeffects,ofcourse,

subsumethedirecteffectofbothofthesevariables.Nevertheless,itispossiblethattheir

impactdiffersinthepre‐andpost‐shockperiods.Column2reportstheinteractionofthese

“quality”variableswiththepost‐1992indicator.Itisnoteworthythatbothofthese

interactionvariablesarenegative(inPanelA),althoughonlythepre‐1992rateofoutputis

statisticallysignificant.

Amoreinterestingspecificationallowsfortheimpactofthese“quality”variablesto

differnotonlypre‐andpost‐shock,butalsobetweenAmerican‐andSoviet‐style

reclassificationandarerobustwhenpaperspublishedinthenewlydefinedsubjectsareremovedfromthesample.

21WedonotobservedirectlyifamathematicianwastenuredatthetimeofthecollapseoftheSovietUnion.The“tenuredasof1992”variableisadummyvariableindicatingifthemathematicianhadatleast10yearsofexperienceasof1992(i.e.,hisfirstpublicationoccurredpriorto1982).Atthetime,post‐doctoralfellowshipsinmathematicswererelativelyrare,sothatamathematicianwhocontinuedtopublishinacademicjournalsafterhisfirstdecadeintheprofessionlikelyhadattainedtenureatanacademicinstitution.

23

mathematicians.ThefullyinteractedmodelpresentedinthethirdcolumnofTable3

reportsthecoefficientsfromthisexpandedspecification.

Considerthevariablemeasuringwhetherthemathematicianwastenuredatthe

timeofthesupplyshockintheregressionthatexaminescognitivemobilitytoa“brandnew”

field.Thethree‐wayinteraction(post‐1992indicator×Soviet‐styledissertation×tenured

asof1992)isstronglynegative,indicatingthattheimpactofthesupplyshockindriving

Soviet‐stylemathematiciansawayfromSoviet‐styleresearchwasattenuatedifthe

mathematicianhadjobsecurityatthetime.22Notethatthenumericalmagnitudeofthis

attenuationeffectislarge:theprobabilityofmovingforthefirsttimetoanAmerican‐style

researchareaaftertheSovietsupplyshockfallsby3.5percentagepointsifthe

mathematicianwastenured.

Similarly,althoughtheinclusionofindividualfixedeffectscontrolsfordifferencesin

individualquality,theremaybeadifferentialeffectbetweenhigh‐andlow‐ability

mathematicians.ThelastcolumnofTable3showsthatthecoefficientofthethree‐way

interactionvariable(post‐1992indicator×Soviet‐styledissertation×rateofoutput)isalso

negativeandsignificant,suggestingthathigh‐abilitySoviet‐stylemathematicianswere

relativelylesslikelytomoveafterthesupplyshock.

Thenumericalmagnitudeofthecoefficientisinteresting.Inparticular,theimpactof

thesupplyshockoncognitivemobilityapproacheszerowhentherateofoutputhasavalue

ofbetween3.5and12.7,dependingonthedefinitionofcognitivemobility.23Thisthreshold

22Note,however,thattheeffectofthe“tenure”variableisonlystatisticallysignificantinthe

regressionthatusesthe'brandnewfield'measureofcognitivemobility.

23Forexample,thecoefficientofthetwo‐wayinteractionbetweenthepost‐1992indicatorandtheSoviet‐styledissertationinPanelBis.216,whilethecoefficientofthethree‐wayinteractionbetweenthesetwovariablesandtherateofoutputis‐.062.Theneteffectiszerowhentherateofoutputis3.5.Therateof

24

roughlymarksthe95thpercentileoftherateofoutputdistributionacrossmathematicians,

sothatthemostprolificSoviet‐stylemathematicianschosetostayinthoselocationsinidea

spacewheretheSovietémigrésclustered.Inshort,theprobabilityofcognitivemobility

rosemarkedlyforthe“average”Soviet‐stylemathematician,butdidnotchange(or

perhapsfell)forhigh‐abilitySoviet‐stylemathematicians.

Insum,thedatarevealthepresenceofapotentiallyimportanttypeofselection:the

cognitivemobilityeffectsofthesupplyshockareattenuatedforthebestAmerican

mathematicianswhodidSoviet‐styleresearch.Thistypeofselectioncanonlyoccurif

eitherthenethumancapitalspilloversarepositiveandverylargeforthemostproductive

Soviet‐stylemathematiciansoriftheirmobilitycostsarerelativelyhigh.Wewilladdress

thesealternativehypothesesinmoredetailinthenextsection.24

ItisworthnotingthattheeffectsdocumentedinTable3arerobusttotheuseof

alternativedefinitionsof“Soviet‐style”fields.Inparticular,Table4re‐estimatesthebasic

setofregressionsusinganumberofalternativedefinitions.Forexpositionalconvenience,

thetoprowofthetablesummarizesthemainsetofcoefficientsresultingfromthesimplest

definition(the10fieldswiththelargestsharesofpapersintheSovietUnionbefore1989),

usingthefullyinteractedspecification.

outputvariabletakesonavalueof3.6atthe90thpercentile,4.7atthe95thpercentile,and7.5atthe99thpercentile.

24IntheappendixofBorjasandDoran(2013a),weextendtheempiricalanalysistoexaminetheevolutionofamathematician’sresearchinterestsoverthelifecycle,andhowthelifecyclepathofresearchinterestswasdisruptedbythesupplyshockinitiatedbythecollapseoftheSovietUnionin1992.WefindthatthesupplyshockreducedthedegreeofcreativediversityoverthelifecycleforAmerican‐stylemathematiciansbecauseitreducedtheirincentivestoengageinSoviet‐styletopics,butincreasedthedegreeofcreativediversityforSoviet‐stylemathematiciansbyencouragingtheirmovetoAmerican‐stylework.

25

Toillustratetheconstructionofthealternativedefinitions,let=sf–af,wheresfis

theshareofpre‐1989paperspublishedinfieldfintheSovietUnion,andafistheshareof

paperspublishedinthatfieldintheUnitedStates.Row2ofthetablereportstheregression

resultswhentheSoviet‐stylefieldsaredefinedasthetenfieldswiththelargestvaluesof

thedifferencedshare.Thereis,ofcourse,asignificantoverlapbetweenthisdefinitionof

Soviet‐stylefieldsandthesimpleroneusedinrow1,butthisalternativedefinitionallows

forthefactthateventhoughafieldlikeOperationsResearch,MathematicalProgramming

waspopularintheSovietUnion,itwasevenmorepopularintheUnitedStates.Despitethe

differenceinthedefinitionofSoviet‐stylefields,theregressioncoefficientsarebarely

affected.

Row3definesthegroupofSoviet‐stylefieldsbyusingthetop10fieldsinthe

relativesharegivenbyR=sf/af.Thisdefinitionisobviouslysusceptibletothepresenceof

“outlier”fields.25Nevertheless,theregressioncoefficientsyieldqualitativelysimilarresults

(althoughwithlargerstandarderrors).Finally,topreventtheclassificationofSoviet‐style

fieldsfrombeingdominatedbyfieldsthatattractaverysmallnumberofAmerican

mathematicians(andhenceleadtoaveryhighvalueofR),row4ofthetableredefinesthe

Soviet‐stylefieldsasthe10fieldsthathavethelargestvaluesoftherelativeshareRaslong

asthefieldhadasignificantpre‐1989Americanpresence(inparticular,afisabovethe

25Forexample,IntegralEquationsaccountedfor1.3percentofSovietpublications,butonlyfor0.3

percentofAmericanpublications,andhasthelargestvalueoftherelativeshare(4.1)

26

median).26Thecomparisonofrows1and4ofthetableagainshowsthattheregression

coefficientsarequantitativelyverysimilar.27

Wealsoconstructedtwodistance‐basedmeasuresofcognitivemobility.Thefirst

usesthesimilarityindexbetweentheresearchinterestsofaparticularAmerican

mathematicianandthepre‐1990Sovietfielddistribution.Letaifbetheshareofpapersthat

Americanmathematicianipublishedinfieldf,andletsfbetheshareofallSovietpapers

publishedinfieldfbeforethecollapseoftheSovietUnion.Theindexofsimilarity(Cutler

andGlaeser,1997)formathematicianiisdefinedby:

(10) Di 11

2aif s f

f .

WecalculatethevalueofthesimilarityindexforeverypaperwrittenbyanAmerican

mathematician.Itiseasytoshowthatthevalueoftheindexofsimilarityforpapern

writtenbymathematicianiinfieldfattimetcollapsesto:

(11) Difn(t)=sf.

Inotherwords,theindexofsimilarityforaparticularpaperissimplythevalueofthe

Sovietshareofthefieldassociatedwiththatpaper.

Wecanusetheprogressionoftheindexofsimilarityacrosspapersoverthelife

cycletomeasurethecognitivedistancetraveled(intermsofthe“Soviet‐ness”ofthe

researchtopic)betweenthedissertationpaperandpapern,andtodetermineifthis

26The31fieldsabovethemedianofafaccountedfor86.7percentofallpre‐1989American

publications.

27Theresultsareunlikelytobeanartifactofdifferentialtrendsinthefundingoffieldsinmathematics.Afterall,mathematiciansrarelyrelyongrantstoproducetheirtheorems.Further,BorjasandDoran(2012,TableIII,PanelD)showthatthecompetitiveforces(whichprovidetheincentiveforcognitivemobilityinthemostaffectedfields)wererobusttotheinclusionofafullsetoffield‐yearfixedeffects.

27

distancewasaffectedbytheSovietsupplyshock.Inparticular,letin(t)=Difn(t)–Dif1(t),

whichissimplythedifferenceinthesharesfbetweenthenthandthefirstpaperina

mathematician’scareer.Weestimatedthegenericregressionmodelinequation(9)by

usingbothin(t)anditsabsolutevalue in (t) asdependentvariables,andusingthe

interactionbetweenthepost‐1992indicatorandthesimilarityindexofthedissertation

paperasthekeyindependentvariable.Theabsolutevaluespecification,ofcourse,

measuresthepresenceofanytypeofmobility(akintousingadummyvariableindicatinga

cognitivemove),whilethesignofinreflectsthedirectionoftheflowofcognitivemovers.

ThetoppanelofFigure3illustratesthetrendintheabsolutevaluemeasureofcognitive

distance.Itshowsanincreasein“distancetraveled”after1992formathematicianswho

wroteaSoviet‐styledissertation.Thebasicregressionspecificationsyield:28

(12) in (t) =i+t+.097(Ti×Dif1) (.008)(13) in(t)=i+t–.098(Ti×Dif1) (.008)Thepositiveinteractioninequation(12)showsthatthecognitivedistancetraveled

betweenthedissertationandthenthpaper(intermsofthepaper’sSovietshare)increases

after1992formathematicianswhowroteamoreSoviet‐likedissertation,evenafter

controllingforindividualandperiodfixedeffects.Putdifferently,Soviet‐style

mathematiciansmovedtoamoredistantlocationinideaspaceafter1992.Thenegative

interactioninequation(13)revealsthedirectionofthatmove:Americanmathematicians

28Theregressionsreportedinequations(12)and(13)includeaquarticinyearsofexperience,and

thestandarderrorsareclusteredattheindividuallevel.

28

whowroteaSoviet‐styledissertationchoseresearchtopicsafter1992thatwereless

congruentwiththeSovietresearchprogram.29

Thesecondmeasureofcognitivedistanceusesthefrequencywithwhichfieldscite

eachothertocreateametricacrossthe73fieldsofmathematics.Specifically,letcfgbethe

shareofcitationsmadebypaperspublishedinfieldftopaperspublishedinfieldg.30The

cognitivedistancetraveledbyamathematicianwhenhemovesfrompublishingapaperin

fieldftoapaperinfieldgcanthenbedefinedas:

(14) fg (cff cfg )

maxg(cff cfg ).

Byconstruction,theindexfgequalszerowhenthemathematician“travels”fromone

paperinfieldftoanotherpaperinfieldf,andreachestheupperlimitofonewhenhe

travelsfromapaperinfieldftoapaperinfieldg,wheregisthefieldleastcitedbypapers

publishedinfieldf.Notethatthereisanimportantconceptualdifferencebetweenthetwo

cognitivedistanceindicesgivenbyand.Theformermeasuresdistanceintermsof

“Soviet‐ness,”whilethelattermeasuresdistanceintermsofintellectualcontent.

Themediancognitivedistancebetweenfieldsfandg(excludingallf=gpairs)

is.99.Infact,onlythe"closest"twopercentof“fieldpairs”havecognitivedistancesof.75

orlower,implyingthatalmostallmathematicalfieldsareequally“intellectuallyfar”from

eachother.Inshort,thedatarevealthatmostfields“spend”almostalloftheircitationson

29Wealsoestimatedfullyinteractedregressionspecificationsthatincludedthetenuredandrateof

outputvariables.ThequalitativeimpactoftheseinteractionsisidenticaltothatreportedinTable4.

30Thecitationsharecfgisobtainedfroma50percentsampleoftheAMSdatabasethatwematchedpaper‐by‐paperwiththeISIWebofScience.TheISIWebofScienceincludesfullinformationonthelistofpublicationsthateachpapercitedinitsreferencessection.Wecalculatethiscitationshareusingthesampleofpaperspublishedbefore1992.

29

paperspublishedinahandfulofverycloselyrelatedfields(andespeciallyinwithin‐field

citations).

Letin(t)denotethecognitivedistancebetweenthenthpaperpublishedby

mathematicianiattimetandthedissertationpaper.PanelBofFigure3illustratesthe

effectoftheshockonthismeasureofcognitivedistanceItisevidentthattherewasapost‐

1992increaseinintellectual“distancetraveled”formathematicianswhowroteaSoviet‐

styledissertation.Thebasicregressionspecificationyields:31

(15) in(t)=i+t+.043(Ti×Si) (.006)Thepositiveinteractionin(15)showsthatthedistancetraveledincreasessignificantly

after1992formathematicianswhowroteaSoviet‐likedissertation,evenaftercontrolling

forindividualandperiodfixedeffects.Putdifferently,weagainfindthatSoviet‐style

mathematiciansmovedtoamoredistantlocationinideaspaceafter1992.32

Finally,itisimportanttodetermineifthecognitivemobilityawayfromSoviet‐style

researchbyAmericanmathematicianswasaresultofanimmigration‐inducedsupply

shockthatspecificallyaffectedtheUnitedStatesorreflectsageneralworldwidetrend

resultingfroman“ideashock”thataffectedSoviet‐stylemathematiciansinallcountries.As

wenotedearlier,nearly10percentoftheactivemathematicsworkforceintheSoviet

Unionemigratedafter1992.Asaresultofthisinflux,the(quality‐adjusted)numberof

31Theregressionreportedinequation(14)againincludesaquarticinyearsofexperience,andthe

standarderrorsareclusteredattheindividuallevel.

32Theresultsareverysimilarifwemeasurecognitivedistanceusingan"indexofdissimilarity"constructedfromthecitationmatrix.

30

mathematiciansintheUnitedStatesincreasedby3.4percent,whiletherespectiveincrease

insupplyoutsidetheUnitedStateswas2.0percent.33

Todetermineifthedifferentialsizeofthesupplyshockshadarelativelylarger

effectonthecognitivemobilityrateofSoviet‐stylemathematiciansintheUnitedStates,we

re‐estimatedtheregressionmodelinequation(9)usingapooledsamplecomposedof

Americanmathematiciansandmathematiciansinthe“restoftheworld.”34Wethen

interactedtheSovietdissertationmeasurewithanindicatorvariableUSAisettounityif

mathematicianiisAmerican.Theexpandedregressionmodelisgivenby:

(16) pin(t)=i+t+(Ti×Si)+(Ti×Si×USAi)+Zi+,

Table5presentstherelevantregressioncoefficientsusingourtwomainmeasures

ofcognitivemobility(basedonthetop10Sovietfields).Itisevidentthattherewasa

higherrateofcognitivemobilityawayfromSoviet‐styleresearchfieldsintheUnitedStates

thanintherestoftheworld.35

33Thepercentincreaseinsupplyisweightedbythenumberofpaperspublishedbythevarious

mathematiciansbetween1987and1991.Thequality‐adjustedmeasureofthesupplyshockisfargreaterthanthepercentincreaseinthenumberofactivemathematicians:theémigréflowonlyincreasedthenumberofmathematiciansby1.1percentintheUnitedStatesand.4percentintherestoftheworld.

34Thesampleofpre‐existingmathematiciansinthe“restoftheworld”consistsoftheresidualsampleofnon‐Americanandnon‐Sovietmathematicians.BecauseitisdifficulttoestablishnationaloriginoutsidetheUnitedStatesandtheSovietUnionforoldermathematicians,werestricttheregressionanalysistomathematicianswhosefirstpaperwaspublishedafter1960.

35Itiseasytocarryoutaback‐of‐the‐envelopecalculationoftheceterisparibusimpactofthesupplyshock(assumingthatthe“ideashock”affectedmathematiciansinallcountriesequally).Inparticular,notethatthereisa1.4percentagepointdifferenceinthesupplyshockbetweentheUnitedStatesandtherestoftheworld.TheinteractioncoefficientreportedinthefirstcolumnofTable5suggeststhatthisdifferencewasresponsiblefora3.1percentagepointrelativeincreaseinthecognitivemobilityrateofAmericanmathematicians.Putdifferently,asupplyshockthatincreasessupplybyonepercentincreasestherateofmobilityby2.2percentagepoints(ortheratioof3.1to1.4).Asaresult,the3.4percentsupplyshockexperiencedbytheUnitedStateswouldbepredictedtoincreasetherateofcognitivemobilityofSoviet‐styleAmericanmathematiciansby7.5percentagepoints.

31

V. The Costs of Cognitive Mobility

Cognitivemobilitymaybecostly.Amathematicianmayneedtoacquireadditional

technicalskillstoprovetheoremsatthenewlocationinideaspace.Thisprocesstakestime

andmayleadtoalonger“preparationspell”(i.e.,theamountoftimethatthe

mathematicianspendspreparingandmarketinganewpublication).Itiseasytodocument,

infact,thatpreparationspellsarelongerifthespellinvolvesaswitchtoanewfield.The

Sovietsupplyshockcouldthenpotentiallyincreasethecostsofcognitivemobilityintwo

distinctways.First,itincreasedthepropensityforcognitivemobilityamongAmerican‐

stylemathematicians.Second,theclusteringoflargenumbersofSovietmathematiciansin

specificlocationsinideaspacecouldincreasethelengthofthepreparationspellfor

cognitivemovers.

Table6summarizessomeoftheavailableevidenceonthelengthofpreparation

spellsforSoviet‐andAmerican‐stylemathematicians,beforeandafterthesupplyshock.36

Wedefinethedurationofapreparationspellasthelengthoftimeelapsed(inyears)

betweenanytwoconsecutivepapersinamathematician’scareer.AsPanelAshows,even

beforethesupplyshock,switchingfieldsinvolvedaslightlylongerpreparationspell.The

preparationspellbetweentwoconsecutiveAmerican‐stylepaperslasted1year,as

comparedto1.2yearsforamovefromAmerican‐toSoviet‐styleresearch.Similarly,the

preparationspellbetweentwoconsecutiveSoviet‐stylepaperswas.8years,butamove

fromSoviet‐styletoAmerican‐styleresearchtook1.1years.

36SincetheevidenceisrobusttothedefinitionofSoviet‐stylefields,weusethesimplestdefinitionin

theremainderoftheanalysis(the10fieldswiththelargestSovietsharesofpre‐1989papers).

32

PanelBshowsthatoneparticulartypeofpreparationspellwasextremelysensitive

totheSovietsupplyshock,namelytheonereportingthedurationofthepreparationspell

forSoviet‐stylemathematicianswhoarewritingtheirfirst‐everAmerican‐stylepaper.The

durationofthisparticulartypeofpreparationspellincreaseddramaticallyfrom2.3years

inthepre‐shockperiodto5.1yearsafterthesupplyshock,oranincreaseof2.8years.In

contrast,thesupplyshockincreasedthedurationoftimeinvolvedinthepreparationofthe

first‐everSoviet‐stylepaperby1.2years(from2.2to3.4years).

Weexaminethesensitivityofthesefindingstocontrollingforvarious

characteristicsbyestimatingtheregressionmodel:

(17) yin(t)=i+t+0(Si×Fin)+1(Ti×Si)+2(Ti×Si×Fin)

+0(Ai×Fin)+1(Ti×Ai)+2(Ti×Ai×Fin)+Zi+,

whereyin(t)isthedurationofthepreparationspellthatculminatedinmathematiciani

publishingpapernattimet;Finisadummyvariableindicatingifthisparticularspellended

withthemathematicianpublishingapaperina“brand‐new”field(i.e.,afieldthathehad

notpreviouslyexplored);andAi=(1–Si).Notethattheregressionincludesbothtimeand

individualfixedeffects.37

Thedataconsistsofapanelthatincludeseachpreparationspellexperiencedby

everypre‐existingAmericanmathematicianinoursample.Table7reportstherelevant

regressioncoefficients.Considerinitiallythesimplestspecificationreportedincolumn1,

whichonlyincludesaquarticinyearsofexperienceinthevectorZ.Thecoefficientsofthe

37Itisworthnotingthattheinclusionofindividualfixedeffectsimplicitlycontrolsforveryfine

differencesinmobilityratesacrossmathematicalfields.Inparticular,itcontrolsfortheeaseofmovingoutofthe“dissertation”fieldevenifthedissertationfieldweredefinedintermsofoneofthe73fieldsreportedintheAMSdata.

33

two‐wayinteractionsbetweenthedissertation’sresearchstyleandtheindicatorof

switchingtoanewfieldareessentiallyidenticalforAmerican‐andSoviet‐style

mathematicians.Thethree‐wayinteractionwiththepost‐1992indicator,however,ismuch

greaterforAmericanmathematicianswhowroteaSoviet‐styledissertation.Thedifference

betweenthesetwocoefficients,whichisapproximatelyaroundayear,indicatesthatour

earlierconclusionbasedontherawdataisunaffectedbytheinclusionofindividualand

yearfixedeffects:Soviet‐stylemathematiciansenteringanewfieldhadasubstantial

(relative)increaseinthedurationofthepreparationspellafterthesupplyshock.38

Thelastcolumnofthetableshowsthatthisincreaseisattenuatedsomewhatfor

high‐abilitymathematicians.Asinthelastsection,weintroduceavariablemeasuringthe

rateofoutputformathematicianipriortothesupplyshock.Thecoefficientsreportedin

thetablesuggestthattheSovietsupplyshockparticularlylengthenedthedurationofthe

preparationspellforlow‐qualitySoviet‐stylemathematiciansmovingtoanentirelynew

locationinideaspaceafter1992.

Insum,notonlyisthereastrongpositivecorrelationbetweenthedurationofthe

preparationspellandthepropensitytoenteranewfield,butthecorrelationincreased

markedlyafterthesupplyshock.Thisobservedincreaseisconsistentwithtwocausal

scenarios:(1)thesupplyshockmadeitrelativelymoredifficultforSoviet‐style

mathematicianstoproduce(and/orsell)output,creatingalongerdowntimeinbetween

publicationsandspurringsomeofthemtoseekanewlocationinideaspace;or(2)the

supplyshockinducedSoviet‐stylemathematicianstocognitivelymove,andthesubsequent

retoolingimpliesthatittookthemlongertoprovetheirfirsttheoremsintheirnewlocation

38Thedifferenceisstatisticallysignificant,withat‐statisticof4.62.

34

inideaspace.Underthefirstscenario,cognitivemobilitydoesnotcausetimelags,butis

rathercausedbythem.Underthesecondscenario,thecausationisreversed.Thenatural

experimentweexploitinthispaperisnotdesignedtodistinguishthesecausalchainsfrom

eachother.Nevertheless,thedatarevealanimportantcorrelationthatwilllikelyplaya

roleinfutureattemptstounderstandthenatureofthecostsofcognitivemobility.

Finally,itisworthreturningtoanimportantquestionregardingtheselectionof

cognitivemovers:WhydidthebestSoviet‐stylemathematiciansexhibitthelowestmobility

ratesinresponsetotheSovietsupplyshock?Aswenotedearlier,thiscorrelationcanbe

explainedintwoways:thebestmathematiciansbenefitedthemostfromthepositive

spilloversgeneratedbytheexpansioninthestockofmathematicalideasand/orthebest

mathematicianshadthehighestcognitivemobilitycosts.Theresultspresentedinthis

section,however,stronglysuggestthatthebestSoviet‐stylemathematicians,infact,faced

relativelylowercognitivemobilitycosts.Asaresult,theevidenceimpliesthatthebeneficial

humancapitalspilloversresultingfromtheSovietsupplyshockmostlikelyaccruedtothe

subsampleofthemostproductiveAmericanmathematicians,andthatthesespillovers

effectivelyneutralizedtheadversecompetitiveeffectsinthisproductivegroup.

VI. Field Choices of New Cohorts

Uptothispoint,wehaveexaminedthecognitivemobilityresponseamong“pre‐

existing”Americanmathematicianstotheeconomicforcesunleashedbythecollapseofthe

SovietUnion.Theempiricalevidenceunambiguouslysuggeststhatthecompetitive

pressuresarisingfromanewabundanceofSoviet‐typemathematiciansledmanypre‐

existingmathematicianstoswitchawayfromthosefields.

35

Obviously,thesameeconomicforceswilllikelyinfluencefieldchoicesfornew

entrantsintotheAmericanmathematicsmarket.39Graduatestudents,astheypreparetheir

dissertationandinvestintheskillsrequiredtobecomespecialistsintheirchosenfields,

willinevitablyconsiderthelong‐termvalueofthevariousoptionsavailable,andwillmake

adecisionbasednotonlyonthesuitabilityofthematchbetweentheirspecificskillsand

thetechnicalrequirementsofparticularfields,butalsoonthemarketabilityofresearchin

specificfields.Thetrendinthenumberofnewmathematicianschoosingtospecializein

Sovietfieldswouldthenprovideindependentevidenceontherelativeimportanceof

competitiveversusspillovereffects.FewernewAmericanmathematicianswillchooseto

produceaSoviet‐styledissertationifcompetitiveforcesdominate,whilemanymorenew

mathematicianswouldproduceSoviet‐styledissertationsiftheproductivitygainsresulting

fromtheSovietsupplyshockaresubstantial.

Weillustratethenatureofthese“cohorteffects”byexaminingthefieldchoiceofthe

firstpaperpublishedbyeachmathematician.Asbefore,wecallthisfieldchoicethe

dissertationfield.40Inordertocontrolfortheeffectofworldwidefadsandknowledge

developments,weuseacontrolgroupofmathematiciansinthe“restoftheworld”—the

mathematicalcommunityoutsidetheUnitedStatesandthe(former)SovietUnion.Recall

thattheSovietsupplyshockincreasedthequality‐adjustednumberofmathematiciansin

39Infact,theAmericanMathematicalSociety's1991‐1992AcademicHiringSurveyreportedthatthe

veryhighunemploymentrateofnewmathematicsdoctoratesatthetimewaspartlyduetothefactthat"citizensofEasternEuropeancountriesandtheformerSovietUnionaccountedfor13%ofallnewly‐hiredfaculty"(McClure,1992).

40Wereplicatedtheanalysispresentedinthissectionusingalternativedefinitionsofthe“first”fieldchoice,includingpaperspublishedinthefirstyear,inthefirstfiveyears,orinthefirsttenyears,andthecohorttrendsarequitesimilar.

36

theUnitedStatesincreasedby3.4percent,whiletherespectiveincreaseinsupplyoutside

theUnitedStateswasonly2.0percent.

Figure3illustratesthetrendinthecohorteffectsamongmathematicianswhofirst

publishedbetween1978and2009.ThefractionofAmericanandnon‐American

dissertationsinSoviet‐stylefieldswasrelativelystablefrom1978throughthelate1980s.

In1978,forexample,32.3percentofAmericandissertationswereinSoviet‐stylefields;by

1989,therespectivefractionwas32.7percent.Beginningaround1990,however,the

relativenumberofSoviet‐styledissertationsproducedbynewAmericanmathematicians

begantodecline,andthisdeclinecontinuedsteadilythrough2007.In2007,forexample,

onlyabout22percentofthedissertationsproducedbynewAmericanmathematicians

wereinSoviet‐relatedfields.

Todetermineifthedifferentialsizeofthesupplyshockshadarelativelylarger

effectonthedissertationfieldchoicesofstudentsintheUnitedStates,Table8reportsa

regressionanalysisshowingthemagnitudeofthecohorteffectsintheUnitedStates

relativetothoseobservedinthecontrolgroup.Thesampleconsistsofalldissertations

writtenbyAmericanmathematiciansandbythecontrolgroup.Thedependentvariableis

anindexofthe“Soviet‐ness”ofaparticulardissertation.Itisevidentthatnewentrantsin

theAmericanmathematicsmarketwrotemanyfewerSoviet‐styledissertationsafter1992

thanmathematiciansinthe“restoftheworld.”Inparticular,thefractionofAmerican

dissertationspublishedafter1992inSoviet‐styletopicsdeclinedby5.5percentrelativeto

thosepublishedabroad.

Finally,thelastcolumnofTable8examinesaninterestingaspectofthedeclinein

thefractionofAmericandissertationswritteninSoviet‐styletopics.Aswehaveseen

37

repeatedly,thecompetitiveeffectsinducedbytheSovietinfluxtendtobeattenuatedfor

“high‐ability”mathematicians.Itwouldbeofinteresttodetermineifaperson’sinnate

productivityalsoinfluencesthefieldchoicemadeatthedissertationstage,andattenuates

thecohorteffectsdocumentedinthissection.

Wedonothaveanysocioeconomicbackgroundvariablesthatmayhintatthe

person’soverallqualityatthetimeofthedissertation.However,aselectgroupofAmerican

mathematicians(about16.7percent)enteredthelabormarketwitha“splash.”In

particular,theypublishedmorethanonepaperintheirentryyear.Wedefineanindicator

variablesettounityifthemathematicianmadeahigh‐volumeentryintothemathematics

professionandestimatearegressionmodeltodetermineifthecohorteffectsaresimilar

amongtheseprolificpublishers.Astheregressionsshow,theprolificAmerican

mathematicianswerearound4.5percentmorelikelytoproduceaSoviet‐styledissertation

priorto1992,andthisgapactuallyincreasedbyanadditional2.3percentagepointsafter

1992.41Aswithourearlierresults,itseemsthathigh‐qualitymathematiciansare

particularlypronetobenefitfromhumancapitalspillovers,andthesebenefitsinfluenced

thechoiceofdissertationfieldforthisselectgroupafter1992.42

Weconcludetheempiricalanalysisbyillustratingtherelativeimpact—alongall

margins—oftheSovietsupplyshockonthecompositionofresearchtopicspursuedbythe

Americanmathematicscommunity.Inparticular,Figure4illustratesthetrendsinthe

41Theeffect,however,isonlymarginallysignificantintheregressionthatusestheprobabilitythat

thedissertationwasinaSoviet‐stylefieldasadependentvariable.Wealsoknowwhichuniversityawardedthemathematician’sdoctoraldegreeforabouthalfoftheAmericansample.Weestimatedsomespecificationsthatincludedaschool‐qualityvariable,buttheresultswerenotrobustlikelybecauseofthesampleselection.

42Notethattheinitialfieldchoiceatthedissertationstageisnotinfluencedbythemobilitycoststhatmustbeincurredwhenmovingfromonelocationtoanotherinthespaceofideas.

38

fractionof“active”mathematicians(i.e.,mathematicianswhopublishedatleastonepaper

duringthespecificyear)whowroteaSoviet‐stylepaperbetween1971and2009.43Itis

evidentthattherewaslittledifferenceintherelativenumberofSoviet‐style

mathematiciansintheUnitedStatesandintherestoftheworldpriorto1990,butthetwo

communitiesdivergedsignificantlyafterthedifferentialsupplyshockresultingfromthe

collapseoftheSovietUnionaffectedtherespectivemathematicalcommunities.

VII. Summary

Economistshavefoundthatgeographicmobility,occupationalmobility,andjob

mobilityareallimportantmechanismsthatthelabormarketusestoadapttosupplyand

demandshocks.Thispaperintroducesthenotionofcognitivemobilityasakey

equilibratingmechanisminthemarketforknowledgeproduction.

Weexaminedempiricallythelaborsupplyshockthatoccurredinthespaceof

mathematicalideasintheUnitedStatesafterthecollapseofSovietcommunism.Our

analysisexploitsthefactthattheinfluxofSovietmathematiciansintotheAmerican

mathematicscommunitywasclusteredinarelativelysmallnumberoffields.The

unbalancednatureofthesupplyshockacrosslocationsinideaspaceallowsustoobserve

theflowsofcognitivemobilityunleashedbythechangedeconomicopportunitiesresulting

fromthesupplyshock.

Weconstructedseveralempiricalmeasuresofcognitivemobility.Regardlessofthe

measure,wedocumentthatthediminishingreturnstospecificresearchareasresulting

fromtheincreaseinsupplydominatedthecognitivemobilitydecisionsofpre‐existing

43The“active”mathematiciansinthepost‐1992periodeitherintheUnitedStatesorintherestof

theworlddonotincludetheSovietémigrés.

39

knowledgeproducers.Thisfindingextendstonewcohortsofmathematicianswhoentered

themarketplaceaftertheSovietsupplyshock.Thenewcohortsincreasinglychose

dissertationtopicsthathadexperiencedarelativelysmallincreaseinsupplyfromthe

Sovietémigrés.Ingeneral,therefore,theevidenceisclear:theSovietsupplyshockledto

cognitivemobilityflowsthatdroveAmericanmathematiciansawayfromthoselocationsin

ideaspacethatreceivedlargenumbersofSovietémigrés.

Ouranalysisalsobeginstoshedlightintotheblackboxofthecognitivemobility

decisionbydelineatingsomeofitsdeterminants.Weconsistentlyobservethathigh‐ability

Soviet‐stylemathematicianswerelesslikelytomovetoadifferentlocationinthespaceof

ideasinresponsetotheSovietsupplyshock.Thisevidencesuggeststhathigh‐ability

mathematicianseitherhavehighercostsofmovementormorepositivenetspilloversto

interactionwithotherknowledgeproducers.Sincehigh‐abilitymathematicianshave

shorterpreparationspellsandasmallerincreaseinthelengthofthosespellsduetothe

supplyshock,theevidenceismostconsistentwiththeconjecturethathigh‐ability

mathematiciansarethemainbeneficiariesofthepositivespillovers.

Althoughourstudyaddressesacentralissueinthedebateoverthecostsand

benefitsofhigh‐skillimmigration,itisdifficulttoinferstraightforwardpolicyimplications

fromtheevidence.Manyofthepotentialgainsfromhigh‐skillimmigrationlikelyarise

becauseofthehumancapitalexternalitiesthathigh‐skillimmigrantscanimpartonthepre‐

existingnative‐bornworkforce.Eventhoughthevastmajorityofpre‐existingAmerican

mathematiciansdidnotbenefitdirectlyfromthepresenceoftheirSovietcompetitors,it

maybethecasethatasmallnumberofhigh‐abilityAmericanmathematiciansdid.Wedo

notyetknowhowtocontrastthemagnitudeofthegainsthataccruedtoasmallnumberof

40

Americanmathematicianswiththelossessufferedbythebulkofthepre‐existing

workforce.Infact,eventhoseAmericanmathematicianswho“votedwiththeirminds”and

movedtonon‐Sovietresearchareasmayhavefertilizedtheirnewneighborhoodsinways

thatarenotyetdetectableormeasurable.Further,eventhoughthevolumeanddirectionof

cognitivemobilityflowsmayhavebeenprivatelyoptimal,theymaynothavebeenthe

outcomeschosenbyasocialplanner:knowledgeproducersignoretheirownexternal

effectswhentheymaketheircognitivemobilitydecision.

Finally,itisimportanttoemphasizethatouranalysisfocusesontheknowledge

productionfunctioninaveryspecificmarketplace:academia.Thereareanumberof

institutionalconstraints(e.g.,tenureandrelativelyinelasticdemand)thatgreatlyconstrain

thenatureofthepotentialgainsfromsupplyshocksintheacademicmarketplace.Itisnot

hardtoimaginethatthesamesupplyshockmighthavehadverydifferentproductivity

repercussionshadittakenplaceinacompetitivelabormarket.

Insum,althoughthestudyofthedeterminantsandconsequencesofcognitive

mobilityisatitsinfancy,theevidencereportedinthispaperdemonstratesthattheflowof

knowledgethataneconomycanproducedependsintimatelyonthedecisionsofknowledge

workerstochangetheirlocationinthespaceofideas.Wesuspectthatfurtherstudyofthe

processofcognitivemobilitywillleadtoagreaterunderstandingofknowledgespillovers,

theknowledgeproductionfunction,andthelong‐termimpactofhigh‐skillimmigrationon

economicgrowth.

41

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44

Figure1.Trendsincognitivemobility,1978‐2009A.Probabilityofpublishinginafielddifferentfromdissertation

B.Probabilityofpublishinginabrandnewfield

Notes:ThesampleconsistsofAmericanmathematicianswhofirstpublishedbefore1992.SeeTable2forthelistoffieldsthatareSoviet‐style;allotherfields,bydefinition,areAmerican‐style.Wesmoothoutthetrendbyusinga3‐yearmovingaverageoftherateofcognitivemobilitycenteredonthemiddleyearintheinterval.The'brandnewfield'variableinPanelBmeasurespublishingforthefirsttimeinoneofthetwocategoriesoffields(Soviet‐styleorAmerican‐style).

0

0.1

0.2

0.3

0.4

0.5

1975 1980 1985 1990 1995 2000 2005 2010

Probab

ilty of p

ublishing pap

er in

non‐disserta

on fie

ld

Year

American‐style disserta on Soviet‐style disserta on

0

0.1

0.2

0.3

1975 1980 1985 1990 1995 2000 2005 2010

Probabilty

of p

ublishing in

a fie

l

d fo

r fir

st

me

Year

American‐style disserta on Soviet‐style disserta on

45

Figure2.Trendsincognitivedistancefromdissertation,1978‐2009

A.Absolutevalueofcognitivedistance(indexofsimilarity)

B.Citation‐basedcognitivedistance

Notes:ThesampleconsistsofAmericanmathematicianswhofirstpublishedbefore1992.CognitivedistanceinPanelAisdefinedasthedifferencebetweentheaverageindexofsimilarityforpaperspublishedinyeartandthedissertation’sindexofsimilarity,whileinPanelBitisdefinedastheaveragecitationdistancebetweenthepaperspublishedinyeartandthedissertation.Wesmoothoutthetrendbyusinga3‐yearmovingaverageofthemeasureofcognitivedistancecenteredonthemiddleyearintheinterval.

0.010

0.015

0.020

0.025

0.030

1975 1980 1985 1990 1995 2000 2005 2010

Absolute

value of chan

ge in

index

of sim

ilarity

Year

American‐style disserta on Soviet‐style disserta on

0.3

0.4

0.5

0.6

0.7

1975 1980 1985 1990 1995 2000 2005 2010

Cita

on‐based cogn

ive

distance

from

disserta

on fie

l

d

Year

American‐style disserta on Soviet‐style disserta on

46

Figure3.Trendsinfieldofdissertationacrosscohorts,1978‐2009

Notes:Thesampleconsistsofallmathematicianswhofirstpublishedbetween1978and2009,andusethesubjectclassificationofthefirstpublishedpapertomeasurethelikelihoodthatthedissertationwasinaSoviet‐stylefield.Wesmoothoutthetrendbyusinga3‐yearmovingaveragecenteredonthemiddleyearintheinterval.The“restoftheworld”doesnotincludemathematiciansintheSovietUnion(pre‐1992)orintheterritoriesencompassedbytheformerSovietUnion(after1992).

0

0.1

0.2

0.3

0.4

0.5

1975 1980 1985 1990 1995 2000 2005 2010

Frac

on with disserta

on in

Soviet‐style

field

Cohort year

United States Rest of world

47

Figure4.AggregatetrendsinpublicationsinSoviet‐stylefields,1978‐2009

Notes:ThesampleconsistsofallmathematicianswhopublishedatleastonepaperduringtheyearandexcludesthesampleofSovietémigrés.The“restoftheworld”doesnotincludemathematiciansintheSovietUnion(pre‐1992)orintheterritoriesencompassedbytheformerSovietUnion(after1992).Wesmoothoutthetrendbyusinga3‐yearmovingaveragecenteredonthemiddleyearintheinterval.

0.25

0.30

0.35

0.40

0.45

1975 1980 1985 1990 1995 2000 2005 2010

Frac

on of m

athema

cian

s publishing in

Soviet‐style fields

Year

United States Rest of world

48

Table1.Summarystatistics,sampleofAmericanmathematicians

Variable:

Allmathematicians

Pre‐1992cohorts

Post‐1992cohorts

Numberofmathematicians 78,684 34,318 44,366 Numberofpapers: Published1940‐2009 711,497 560,262 151,235Published1940‐1991 330,370 330,370 ‐‐‐Published1992‐2009 381,127 229,892 ‐‐‐

PercentofpapersinSovietfields: Published1940‐2009 .315 .326 .271Published1940‐1991 .334 .334 ‐‐‐Published1992‐2009 .298 .316 ‐‐‐

Dissertationpaper: PercentofdissertationsinSovietfields .281 .320 .251

Notes:ThesampleconsistsofallAmericanmathematicianswhofirstpublishedbetween1940and2009.The“dissertation”paperisdefinedtobethefirstpaperpublishedbyamathematician.

49

Table2.MainfieldsofpublicationsintheSovietUnion,1984‐1989

Field:

ShareofpaperspublishedintheSovietUnion

ShareofpaperspublishedintheUnitedStates

1.Partialdifferentialequations 0.104 0.0332.Ordinarydifferentialequations 0.074 0.0193.Quantumtheory 0.068 0.0594.Probabilitytheoryandstochasticprocesses 0.061 0.0395.Globalanalysis,analysisonmanifolds 0.048 0.0396.Operationsresearch,mathematicalprogramming 0.044 0.0717.Numericalanalysis 0.043 0.0438.Operatortheory 0.031 0.0199.Statisticalmechanics,structureofmatter 0.029 0.02610.Functionsofacomplexvariable 0.028 0.015Notes:Thepapercountsineachfieldareobtaineddirectlyfromtheweb‐basedAMSMathematicalReviewsdatabase(MathSciNet)andconsistofallpaperspublishedbymathematiciansaffiliatedwithSovietorAmericaninstitutionsbetween1984and1989.

50

Table3.EffectoftheSovietsupplyshockontherateofcognitivemobility Specification

(1) (2) (3)A.Dependentvariable=Paperinafielddifferentfromthedissertation

Post‐1992indicator×Soviet‐styledissertation .123 .125 .140 (.006) (.006) (.014)Post‐1992indicator×Tenuredasof1992 ‐‐‐ ‐.002 ‐.007 (.006) (.006)Post‐1992indicator×rateofoutput ‐‐‐ ‐.007 ‐.003 (.003) (.002)Post‐1992indicator×Soviet‐styledissertation× Tenuredasof1992 ‐‐‐ .009 (.012)Rateofoutput ‐‐‐ ‐0.011

(.006) B.Dependentvariable=Paperinabrandnewfield Post‐1992indicator×Soviet‐styledissertation .130 .124 .216 (.007) (.007) (.015)Post‐1992indicator×Tenuredasof1992 ‐‐‐ .001 .003 (.004) (.004)Post‐1992indicator×rateofoutput ‐‐‐ ‐.015 ‐.010 (.002) (.001)Post‐1992indicator×Soviet‐styledissertation× Tenuredasof1992 ‐‐‐ ‐‐‐ ‐.035 (.012)Rateofoutput ‐‐‐ ‐‐‐ ‐.062

(.010)Notes:Standarderrorsarereportedinparenthesesandareclusteredattheindividuallevel.Thesampleconsistsofmathematicianswhosefirstpublishedpaperwasbefore1992.Allregressionsincludeavectorofindividualfixedeffects,andaquarticcontrolforyearsofexperience.The“tenuredasof1992”variableindicateswhetherthemathematicianhadatleast10yearsofexperienceasof1992;the“rateofoutput”variablegivestheannualnumberofpaperspublishedbythemathematicianbetweentheyearofentryand1991.TheregressionsinPanelAhave525,944observations;theregressionsinPanelBhave216,657observations.TheregressionsinPanelBexcludeallspellsafterthemathematicianfirstswitchestoafielddifferentfromthedissertation.

51

Table4.SensitivityofregressionresultstoalternativedefinitionsofSoviet‐stylefields

=post‐1992indicator×Soviet‐styledissertation

DependentvariableanddefinitionofSoviet‐stylefields:

×Tenured

×Rateofoutput

A.Paperinafielddifferentfromdissertation

1.Toptensovietshares(sf) .140 .009 ‐.011 (.014) (.012) (.006)2.Toptendifferenceinshares(sf–af) .137 ‐.013 ‐.006 (.015) (.013) (.006)3.Toptenrelativeshares(sf/af) .097 ‐.020 ‐.007 (.025) (.022) (.010)4.Toptenrelativeshares(sf/af)andafisabovemedian

.133 ‐.005 ‐.007

(.014) (.013) (.006) B.Paperinabrandnewfield 1.Toptensovietshares(sf) .217 ‐.035 ‐.062 (.015) (.012) (.010)2.Toptendifferenceinshares(sf–af) .297 ‐.089 ‐.072 (.024) (.019) (.014)3.Toptenrelativeshares(sf/af) .346 ‐.077 ‐.058 (.092) (.061) (.010)4.Toptenrelativeshares(sf/af)andafisabovemedian

.274 ‐.080 ‐.069

(.022) (.016) (.013)Notes:Standarderrorsarereportedinparenthesesandareclusteredattheindividuallevel.Thesampleconsistsofmathematicianswhosefirstpublishedpaperwasbefore1992.Allregressionsincludeavectorofindividualfixedeffects,andaquarticcontrolforyearsofexperience.The“tenuredasof1992”variableindicateswhetherthemathematicianhadatleast10yearsofexperienceasof1992;the“rateofoutput”variablegivestheannualnumberofpaperspublishedbythemathematicianbetweentheyearofentryand1991.TheregressionsinPanelAhave525,944observations;theregressionsinPanelBhave216,657observationsinrow1,255,953observationsinrow2,360,091observationsinrow3,and256,737observationsinrow4;TheregressionsinPanelBexcludeallspellsafterthemathematicianfirstswitchestoafielddifferentfromthedissertation.

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Table5.TherelativeimpactoftheSovietsupplyshockonAmericanmathematicians Dependentvariable

Variable:

Paperinafielddifferentfromthedissertation

Paperinabrandnew

fieldPost‐1992indicator×Soviet‐styledissertation .094 .110 (.003) (.003)Post‐1992indicator×Soviet‐styledissertation× Americanmathematician .031 .021 (.007) (.007)

Notes:Standarderrorsarereportedinparenthesesandareclusteredattheindividuallevel.Thesampleconsistsofmathematicianswhosefirstpublishedpaperwasbefore1992.Allregressionsincludeavectorofindividualfixedeffects,andaquarticcontrolforyearsofexperience.Theregressioninthefirstcolumnhas1,909,179observations,andtheregressioninthesecondcolumnhas869,849observations.Theregressionthatusesthe“brandnewfield”dependentvariableexcludesallspellsafterthemathematicianfirstswitchestoafielddifferentfromthedissertation.Theregressionsexcludethesampleofpre‐existingSovietmathematicians(bothémigréandnon‐émigré).

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Table6.Summarystatisticsonthedurationofpreparationspells

Spellendsbefore1992with:

Spellendsafter1992with:

American‐stylepaper

Soviet‐stylepaper

American‐stylepaper

Soviet‐stylepaper

A.Spellstartswith: American‐stylepaper .963 1.221 1.156 1.295Soviet‐stylepaper 1.122 .756 1.294 .770

B.Spellinvolvestransitiontoanewfieldandthedissertationwas:

American‐style ‐‐‐ 2.195 ‐‐‐ 3.418Soviet‐style 2.289 ‐‐‐ 5.074 ‐‐‐

Notes:Apreparationspellisdefinedasthelengthoftimeelapsedbetweenamathematician’sconsecutivepapers(inyears).ThesampleconsistsofAmericanmathematicianswhosefirstpublishedpaperwasbefore1992.

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Table7.EffectoftheSovietsupplyshockonthedurationofpreparationspells

SpecificationIndependentvariable: (1) (2)Soviet‐styledissertation×Newfieldatendofspell .790 .194 (.054) (.086)Soviet‐styledissertation×Newfieldatendofspell×: Post‐1992indicator 1.340 2.852 (.162) (.285)

Soviet‐styledissertation×Newfieldatendofspell×post‐1992indicator×:

Tenuredasof1992 ‐‐‐ .365 (.500)Rateofoutput ‐‐‐ ‐1.341 (.227)

American‐styledissertation×Newfieldatendofspell .738 .398 (.045) (.082)

American‐styledissertation×Newfieldatendofspell×: Post‐1992indicator .454 1.368 (.104) (.187)

American‐styledissertation×Newfieldatendofspell×post‐1992indicator×:

Tenuredasof1992 ‐‐‐ .103 (.244)Rateofoutput ‐‐‐ ‐.807 (.123)

Notes:Standarderrorsarereportedinparenthesesandareclusteredattheindividuallevel.Thesampleconsistsofmathematicianswhosefirstpublishedpaperwasbefore1992.Theregressionshave525,944observations.The“newfieldatendofspell”variableissettounityifthespellconcludedwiththemathematicianpublishingapaperinafieldwherehehadneverpublishedbefore;the“tenuredasof1992”variableindicateswhetherthemathematicianhadatleast10yearsofexperienceasof1992;andthe“rateofoutput”variablegivestheannualnumberofpaperspublishedbythemathematicianbetweentheyearofentryand1991.Allregressionsincludethemathematician’sexperience(definedasafourth‐orderpolynomial),avectorofindividualfixedeffects,andavectorofyearfixedeffects.Theregressionsalsoincludeallrelevantsmaller‐orderinteractionsbetweenthetenuredandrateofoutputvariablesandthedissertationstyleindicator,thenewfieldindicator,andthepost‐1992indicator.

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Table8.EffectoftheSovietsupplyshockonthedissertationfieldofsuccessivecohortsofAmericanmathematicians

Comparisongroup

Variables: Restofworld AmericansonlyA.Soviet‐styledissertation Americanmathematician ‐.006 ‐‐‐ (.005) Americanmathematician×post‐1992indicator ‐.055 ‐‐‐ (.006) Prolificmathematician ‐‐‐ .045 (.011)Prolificmathematician×post‐1992indicator ‐‐‐ .023 (.014)

A.Similarityindexofdissertation(10) Americanmathematician ‐.010 ‐‐‐ (.002) Americanmathematician×post‐1992indicator ‐.027 ‐‐‐ (.004) Prolificmathematician ‐‐‐ .035 (.006)Prolificmathematician×post‐1992indicator ‐‐‐ .017 (.007)

Notes:Standarderrorsreportedinparenthesesandareclusteredbyyearofentry.Theregressionsusethesampleofmathematicianswhosefirstpublicationwasbetween1978and2009.ThedependentvariableinpanelAisadummyvariableindicatingifthemathematician’sdissertationwasinaSovietfield,whilethedependentvariableinpanelBisthesimilarityindexassociatedwiththemathematician’sdissertation.Thedummyvariableindicatingifthemathematicianis“prolific”issettounityifthemathematicianpublishedmorethanonepaperintheyearheenteredthemathematicscommunity.Theregressionshave391,408incolumn1and64,290observationsincolumn2.Allregressionsincludeavectorofyear‐of‐entryfixedeffects.

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Appendix I. Creative Diversity Over the Life Cycle

TheempiricalanalysisdemonstratesthatAmericanmathematicianswhowroteaSoviet‐styledissertationweremuchmorelikelytomovetoresearchactivitiesonAmerican‐styletopicsafter1992.Wenowexaminetheevolutionofamathematician’sresearchinterestsoverthelifecycle,andhowthelifecyclepathofresearchinterestswasdisruptedbythesupplyshockinitiatedbythecollapseoftheSovietUnionin1992. ItisinstructivetothinkoftwodistinctwaysofsummarizinghowthecognitivemobilitydocumentedinSectionIIIaffectsthelifecyclepathofresearchchoices.Attimet,forexample,thefieldcompositionofamathematician’spublicationsinthatparticularyearshouldreflecttheimpactofthevariousmovesinideaspacethathavetakenplaceuptothatpointinthelifecycle.Inaddition,wecanalsodefineacumulativemeasureofamathematician’sresearchinterestsbyexaminingthefieldcompositionofallpapersthathehaspublisheduptoandincludingtimet. WeestimatearegressionmodelthatallowsustoquantifytheimpactoftheSovietsupplyshockontheaging‐specializationprofile.Weaggregatedthedatasetconstructedearliertotheauthor‐yearunitofanalysis,sothatanobservationrepresentsanauthor‐yearcombination.Byconstruction,anobservationforaparticularmathematicianexistsonlyinthoseyearswherethemathematicianhaspublishedatleastonepaper.Wefirstexamineameasuresummarizingthefieldmixofpaperspublishedbytheauthorattimet.Asnotedabove,thelocationofamathematicianinideaspaceattimetistheendresultofallthecognitivemobilitydecisionsmadebythemathematicianpriortoandincludingtimet.Wewishtodeterminehowthefieldmixataparticularpointintimechangesoverthecycle,andifthisagingprofilewasdisplacedbytheSovietsupplyshockin1992.Letxidenotemathematiciani’syearsofexperience,definedasthenumberofyearselapsedbetweenthetimethemathematicianfirstpublishedandtimet.Weestimatetheregressionmodelgivenby:(A‐1) it=i+t+1(xi×Si)+2(xi×Ti×Si)

+1(xi×Ai)+2(xi×Ti×Ai)+,whereitisthefractionofpaperspublishedbymathematicianiincalendaryeartthatareSoviet‐style.Thecoefficientsofinterestarecontainedinthevector[1,2,1,2].Thisvectorsummarizeshowtheage‐specializationprofilesdifferbetweenSoviet‐andAmerican‐stylemathematicians,aswellasbeforeandaftertheSovietsupplyshock.Notethattheinclusionofindividualandcalendaryearfixedeffectsimpliesthatthedifferentialimpactoftheshockonfieldchoiceisidentifiedfromvariationwithinindividuals(aftercontrollingforwhatevercommon“fads”mayexistinfieldchoiceovertime). Weestimateequation(A‐1)bydefiningexperienceasafourth‐degreepolynomial.Thevectorofcoefficientsofinterest,therefore,isnoteasytointerpret(butthecoefficientsarereportedinAppendixTableA‐1).Theresultsaremucheasiertounderstandbytracingouttheage‐specializationprofilesimpliedbytheestimatedcoefficients.PanelAof

57

AppendixFigureA‐1illustrateshowtheageprofilesdifferamongthefourgroupsofinterest.44

ItisevidentthatthedifferentratesofcognitivemobilitybetweenAmerican‐andSoviet‐stylemathematiciansbeforeandaftertheSovietsupplyshockcreatesignificantdifferencesintheirage‐specializationprofilesaswell.TheageprofileofAmerican‐stylemathematicianswasroughlythesamebeforeandafter1992,althoughthereisatendencyfortheAmerican‐stylemathematicianstopublishslightlyfewerSovietpapersatagivenlevelofexperienceafter1992.However,thefigureillustratesadramaticdifferenceintheage‐specializationprofileofSoviet‐stylemathematiciansbeforeandaftertheshock.Inparticular,theprobabilitythataSoviet‐stylemathematicianpublishedaSoviet‐stylepaperinthe20thyearofexperiencefellbyabout10percentagepointsaftertheshock.

Inadditiontotheimpactofpriorcognitivemobilitydecisionsonthefieldmixofpaperspublishedattimet,itisalsointerestingtoexaminethecumulativeimpactofthevariousmovesinideaspaceonthefieldmixofamathematician’sentirelifeoeuvre.Inparticular,whatfractionofallthepapersthatamathematicianhaspublishedbythetimehehasxyearsofexperienceareinSoviet‐stylefields,andhowwasthiscumulativesummarymeasureaffectedbytheSovietsupplyshock?

Were‐estimatedtheregressionmodelin(A‐1)usingadependentvariablethatgivesthefractionofpaperspublishedbyyeartthatconductSoviet‐styleresearch.45PanelBofAppendixFigureA‐1illustratestheage‐specializationprofilesimpliedbytheestimatedcoefficients.Notsurprisingly,thecumulativeimpactoftheshockdampensthegrowththatwouldhaveotherwiseoccurredamongAmerican‐stylemathematiciansinthefractionofamathematician’scumulativeworkthatdabbledinSoviet‐styletopics.Inotherwords,forAmerican‐stylemathematicians,theevidencesuggeststhattheSovietsupplyshockreducedthedegreeofcreativediversityintheirlifeoeuvrebecauseitreducedincentivestoengageinSoviet‐styletopics.Incontrast,thefigureshowsareductioninthefractionofcumulativepapersthatinvolveSoviet‐styleresearchformathematicianswhostartedoutwithaSoviet‐styledissertation.Putdifferently,thesupplyshockincreasedthedegreeofcreativediversitythatSoviet‐stylemathematiciansexperiencedovertheirlifecycle.

44Thepredictedspecializationratesarenormalizedtoequalzeroforallgroupsatthebeginningof

thelifecycle.

45Thisregressionusesa“filledin”author‐yeardatasetthatcontainsanobservationforeachyearofanactivemathematician’slife(regardlessofwhetherhepublishedornot)sincewecanobservethecumulativefielddistributionatanypointintime.Thepanelincludesallannualobservationsbetweentheyearofthemathematician’sfirstpublicationandthe15thyearafterthemathematician’slastpublication.

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Appendix II. Data Construction

Thedatausedtoconstructourdependentandindependentvariablesaredrawnfromasingledatabase:theuniverseofpublicationsinmathematicsasarchivedbytheAmericanMathematicalSociety(AMS)MathematicalReviews.Inordertodefineasampleof“American”mathematicianswhowereactiveintheAmericanmathematicalmarketbefore1984,wealsousedatadrawnfromtwoadditionaldatabases:theThomsonReuters’ISIWebofSciencearchive;andtheMathematicalGenealogyProject(MGP)datathatlinksnewdoctoraldegreesgrantedinmathematicstotheirdoctoraladvisors.1.AMSMathematicalReviews

AMSMathematicalReviewsrecordsthetitles,publicationsources,authornames,references,fields,andcitationsofover2millionarticlesfrom2,764differentjournalsandpublicationsourcesworldwide.TheeditorsofMathematicalReviewsalsorecordsubjectclassificationcodesforeachpaperinitsdatabase:64subfieldsdefinedaccordingtothe2‐digit2010MathematicsSubjectClassification(MSC2010),104subfields(3‐digitMSC),or610subfields(5‐digitMSC).Weusethe2‐digitcodingthroughout.Beginningintheearly1980s,thearchivalrecordofeachpublishedpaperprovidesinformationnotonlyontheauthorandthefieldofthepaper,butalsoontheauthor’saffiliationatthetimethepaperwaspublished.

TheAMSprovideduswithaspreadsheetcontainingthepublicationhistoryofallmathematicianssince1939.Arowinthisspreadsheetdefinesaparticularpermutationofauthor(i),field(j),andyear(t).Foreach(i,j,t)rowwehaveinformationon:thenumberofpaperspublished;theinstitutionalaffiliation(s)associatedwiththepapersinthatrow;andthe(country)locationoftheaffiliation(s).2.ThomsonReuters’ISIWebofScience

TheISIWebofSciencerecordsthetitles,publicationsource,authornames,references,andcitationsofmillionsofarticlesfromthousandsofjournalsworldwide.Formanyarticles(especiallyafter1978),thedatabaserecordsresearchaddressesandreprintaddressesforeachauthor.Wepurchasedtherecordsofall1.2millionarticlesintheprimaryISIWebofSciencedatabasebetween1970and2009forthefollowingcategories:Mathematics,AppliedMathematics,InterdisciplinaryApplicationsofMathematics,MathematicalPhysics,andStatistics&Probability.Wealsopurchasedtherecordsofall1.9millionarticlesreferencedbythesemainarticles,andthe2.4millionpapersthatcitethesemainarticles.WeobtainedspecialpermissionfromtheAMStomergeourISIpapersbytitle,source,andauthorwiththeAMSdatabase.Thevariablesanalyzedinthispaperarenotdrawnfromthematchedsample.TheISIdataareusedtosimplygatherlocationinformation(between1978and1984)formathematicianswhodonotreportanypost‐1984locationintheAMSdatabase.3.MathematicsGenealogyProject(MGP)

Fordoctoraldegreesawardedinmathematics,theMGPdatabasereportsthenameofthedegreerecipient,thenameofthedoctoraladvisor,theyearinwhichthedegreewascompleted,andthenameoftheinstitutiongrantingthedegree.Inadditiontothesedata,

59

theMGPalsoprovideduswitheachadvisor’sandstudent’sAMSuniqueauthoridentifier.TheidentifierallowsustomergeMGPdatabasewiththeAMS/ISIdatabases,andobtainalltheavailableinformationonthepublicationandcitationrecordsofbothstudentsandadvisors.TheuniqueAMSidentifiersareavailableforabout65percentofdegreesawardedsince1960.

4.ConstructionofthesampleofpredominantlyAmericanmathematicians Wefocusonasampleofmathematicianswhosefirstpublishedpaperoccurredonorafter1940.ThedatabaseprovidedtousbytheAMSreportsthemathematician’sinstitutionalaffiliationandlocationforanyyearthatthemathematicianpublishedatleastonepaper.InBorjasandDoran(2012),weusedtheAMSdatatoidentifythenumberoftimesthatthereportedinstitutionalaffiliationpriorto1989waslocatedintheUnitedStates.WesupplementedtheinformationavailableintheAMSdatabyusingboththeISIandtheMGPdatatodefinethesampleofpredominantlyAmericanmathematicians.Asnotedabove,theISIdatacontainsaffiliationandlocationinformationformanyotherpublishedpapersbetween1978and1983.Weusethislocationinformationiftheequivalentpost‐1984dataarenotavailableintheAMS.Finally,theMGPdatabasereportstheinstitutionwherethemathematicianreceivedthedoctoraldegree.Amathematicianisthenclassifiedas“predominantlyAmerican”iftheAMS/ISIlocationdataindicatethatmorethanhalfoftheaffiliationsofpublicationpriorto1989werelocatedintheUnitedStates.IfthepooledAMS/ISIdatadonotprovideanyinformationonthelocationofthemathematicianpriorto1989,weassumethatamathematicianwhoreceivedadoctoraldegreeintheUnitedStatesbetween1950and1977isaffiliatedwithanAmericaninstitutionandhe,too,isclassifiedaspredominantlyAmerican. WeemployedthisapproachtodefinethesampleofpredominantlyAmericanmathematicianswhofirstpublishedafter1989.Inparticular,weexaminedtheaffiliationdataintheAMSavailableforpaperspublishedinthefirstfiveyearsofthecareer,andclassifyapersonaspredominantlyAmericanifmorethanhalfofthepaperspublishedinthatintervalusedanAmericanaffiliation.Weusedasimilarapproachtodefinethebaselinesampleofnon‐AmericanmathematiciansusedinthecohortanalysisreportedinSectionVII.

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APPENDIXFIGUREA‐1.Theevolutionoffieldspecializationoverthelifecycle

A.FractionofpaperspublishedinSoviet‐stylefieldsattimet

B.FractionofpaperspublishedinSoviet‐stylefieldsuptotimet\

Notes:ThesampleconsistsofAmericanmathematicianswhofirstpublishedbefore1992.Theage‐specializationprofilesarepredictedusingtheregressionmodelinequation(A‐1);theestimatedlifecycleprofilesarereportedinAppendixTableA‐1.Seetextfordetails.

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APPENDIXTABLEA‐1.Age‐specializationprofiles DependentvariableIndependentvariable:

(1)Percentofpaperspublishedattimet thatareSoviet‐style

(2)Percentof papersuptotimet thatareSoviet‐style

Ai×:

Ti ‐0.021 ‐.010

(.006) (.001)Experience .118 .167 (.016) (.002)Experience2 ‐.080 ‐.106 (.016) (.002)Experience3 .024 .030 (.006) (.001)Experience4 ‐.0026 ‐.003

(.001) (.0001)Ai×Ti×:

Experience ‐.029 ‐.098 (.030) (.005)Experience2 .034 .080 (.025) (.004)Experience3 ‐.014 ‐.025 (.008) (.001)Experience4 .002 .003

(.001) (.0001)Si×:

Ti ‐‐‐ ‐‐‐

Experience ‐.206 ‐.319 (.023) (.004)Experience2 .071 .190 (.026) (.004)Experience3 ‐.013 ‐.054 (.010) (.002)Experience4 .001 .006

(.001) (.0002)Si×Ti×:

Experience ‐.146 .131 (.042) (.006)Experience2 .074 ‐.128 (.038) (.006)Experience3 ‐.018 .043 (.013) (.002)Experience4 .002 ‐.005 (.002) (.002)

Notes:Standarderrorsarereportedinparentheses.“Yearsofexperience”isdefinedasthenumberofyearselapsedattimetsincethefirstpublication,isdividedby10,andisdemeaned.ThevariableSiissettounityif

themathematician’sdissertationwasinaSovietfield;Ai=1–Si;andTiisadummyvariableindicatingifthe

observationrepresentsayearafter1992.Theregressionshave199,251observations(column1)and627,978observations(column2).Allregressionsincludeavectorofindividualfixedeffectsandavectorofcalendaryearfixedeffects.