NETWORK STRUCTURE AND HUMAN CAPITAL DYNAMICS
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NETWORK STRUCTURE AND HUMAN CAPITAL DYNAMICS Tiago V. V. Cavalcantiy Chryssi Giannitsarouz November 9, 2011 Abstract. We study how network structure a?ects the dynamics of human capital, growth and inequality. We do this by explicitly embedding networks into an otherwise standard endogenous growth model with overlapping generations, in which human capital depends on four factors, namely (i) investment in education, (ii) inter- generational transmission, (iii) a global externality and (iv) a local externality that is determined by the network structure. We show that if the population is heterogeneous initially, then there exists a balanced growth path with no inequality and its local sta- bility depends on the network at hand, summarized by a measure of network cohesion. As network cohesion increases, the parameter region for which the balanced growth path is stable becomes larger; i.e. it becomes more likely that society will converge to a path of long run equality. We also ?nd that during the transition, growth is high and inequality is low when regions with the highest initial human capital are located at central nodes of the network. As an illustration, we use school and income data from six Swiss cantons and show that our model, which explicitly takes into account the network structure of a canton, performs better at explaining income data than one that does not.
- networks into
- human capital
- growth path
- community structure
- rates depend
- positive correlation
- economic growth
- local externality
- depends
NETWORKSTRUCTUREANDHUMANCAPITALDYNAMICS
TiagoV.V.Cavalcanti
y
ChryssiGiannitsarou
z
November9,2011
Abstract.
Westudyhownetworkstructurea¤ectsthedynamicsofhuman
capital,growthandinequality.Wedothisbyexplicitlyembeddingnetworksintoan
otherwisestandardendogenousgrowthmodelwithoverlappinggenerations,inwhich
humancapitaldependsonfourfactors,namely(i)investmentineducation,(ii)inter-
generationaltransmission,(iii)aglobalexternalityand(iv)alocalexternalitythatis
determinedbythenetworkstructure.Weshowthatifthepopulationisheterogeneous
initially,thenthereexistsabalancedgrowthpathwithnoinequalityanditslocalsta-
bilitydependsonthenetworkathand,summarizedbyameasureofnetworkcohesion.
Asnetworkcohesionincreases,theparameterregionforwhichthebalancedgrowth
pathisstablebecomeslarger;i.e.itbecomesmorelikelythatsocietywillconvergeto
apathoflongrunequality.Wealsondthatduringthetransition,growthishigh
andinequalityislowwhenregionswiththehighestinitialhumancapitalarelocated
atcentralnodesofthenetwork.Asanillustration,weuseschoolandincomedata
fromsixSwisscantonsandshowthatourmodel,whichexplicitlytakesintoaccount
thenetworkstructureofacanton,performsbetteratexplainingincomedatathanone
thatdoesnot.
Keywords:
Humancapital,growth,inequality,localexternality,networks
JELClassification:
O40,E24,D62,D85
WearegratefultoAqibAslam,PaulBeaudry,VascoCarvalho,EdouardChalle,DeanCorbae,Tom
Crossley,TatianaDamjianovic,ParthaDasgupta,AlessandraFogli,SanjeevGoyal,JonathanHeathcote,
MigelLeon-Ledesma,MarcovanderLeij,OmarLicandro,YanLiu,HamishLow,KjetilStoresletten,José
Tavares,RichardTodd,FrederikToscani,FlavioToxvaerd,andKlausWaeldeforinterestingconversations
andusefulcommentsonthisproject.Wealsothankparticipantsatthe2ndCambridge-Oxford-London
MacroMeeting,the2009SAETmeeting,18thCEPRESSIM,the10thCRETEconference,andsemi-
narparticipantsatUniversityofManchester,UniversityofCopenhagen,UniversityofIllinoisinUrbana-
Champaign,UCDavis,SUNYinStonyBrook,UniversityofOxford,CREIBarcelona,UniversitatAu-
tonomadeBarcelona,FederalReserveBankofMinneapolis,UniversityofGlasgow,UniversityofBristol,
CopenhagenBusinessSchoolandCityUniversityLondon.PartofthispaperwascompletedduringChryssi
GiannitsarousvisittotheFederalReserveBankofMinneapolissheisgratefulfortheirhospitality.
y
FacultyofEconomicsatUniversityofCambridge.
E-mail
:tvdv2@cam.ac.uk.
z
FacultyofEconomicsatUniversityofCambridgeandCEPR.
E-mail
:cg349@cam.ac.uk.
1
CavalcantiandGiannitsarou
2
1.Introduction
Whatistheimportanceofnetworkstructuresforhumancapitalaccumulationandthusfor
economicgrowthandinequality?Weinvestigatehowsocietiesthatarepopulatedbyagents
withdi¤erentinitialhumancapitallevels,butareotherwiseidenticalintermsofeconomic
primitivessuchaspreferences,technologyandendowment,canhavedi¤erentequilibrium
dynamicsandlongrunbehavior,dependingonwhetherandhoweconomicagentsarelinked.
Ourmodelisastylizedeconomywithoverlappinggenerations,inwhichparentsinvestin
theeducationoftheiro¤spring.Akeyingredientofouranalysisistheevolutionofhuman
capital:weassumethatfuturehumancapitaldependsonfourdistinctfactors,namely
investmentineducation,intergenerationalhumancapitaltransmission(inheritedcapital),
a
global
externality(educationsystemorcommonschoolcurriculumintheeconomy)and
nallyona
local
externality.Ournoveltyisinthewaythatthelocalexternalityismodeled.
Wedescribethesocialstructurebyanetworkandassumethatthelocalexternalityis
asummarystatisticofthehumancapitalofaregionsneighborsinthenetwork,e.g.the
averagehumancapitaloftheneighbors.Inthisway,wehaveanoperationalframeworkwhere
di¤erencesinsocialstructuresmaya¤ectindividualoutcomesthroughlocalexternalities,
sincethereturnoninvestmentineducationdependsonregionalconnections.
1
Themainndingsofthepaperarethefollowing.First,ifthepopulationishomogenous
inallrespects,i.e.everyonehasthesameinitialhumancapital,thenthenetworkstructure
isirrelevantforhumancapitaldynamicsandtheeconomyisalwaysonastablebalanced
growthpathwithequality(thereisnouncertaintyinthemodel)irrespectiveofthenetwork
structure.Second,weshowthatifthepopulationisheterogeneouswithrespecttoinitial
humancapital,butidenticalinallotherdimensions,thenthelongrunbehaviorofthe
economydependsonthenetworkstructureinanon-trivialway.Weshowthatforthe
economytoconvergetoabalancedgrowthpathwithlongrunequality,aconditionneeds
tobesatisedthatrelatestheimportanceoftheexternalitiesandnetworkstructuretothe
importanceofinvestmentineducation.Inparticular,forconvergencetoabalancedgrowth
pathwithlongrunequality,notonlydoweneedstrongglobalandlocalexternalities,
butalsothattheeconomyhasacohesivenetworkstructure,inasensethattobemade
precise.Indeed,astheeconomybecomesmorecohesive,longrunequalityprevailsfora
largerrangeofexternalityparameters.Weprovethisbycarefullydeninganappropriate
measureof
networkcohesion
andthenshowhowitdeterminestheparameterregionsfor
whichthebalancedgrowthpathwithequalityislocallystable.Thismeasureisasummary
statisticthatcapturesthevariabilityoftheintensitywithwhichnetworknodes(i.e.regions
andhouseholds)interactwitheachother.Wealsoshownumericallythatwhenthetwo
externalitiesareweakandthenetworkcohesionislow,thereexistbalancedgrowthpaths
withlongruninequality,wherethegrowthratesdependonthenetworkstructure,andare
1
Inthisrespect,ourpaperborrowstheideafromColeman(1988)thatsocialcapitalornetworksmight
beanimportantinputintheformationofhumancapital.
NetworkStructureandHumanCapitalDynamics
3
alwayshigherthanthegrowthratethatcorrespondstolongrunequality.
Tostudytransition,wecalibratethemodeltotheSwisseconomy.Welookatthe
transitiontowardsthebalancedgrowthpathwithequalitybyperformingexperimentsthat
resembleimpulseresponseanalysis.Specically,weassumethatatthebeginningoftime,
theeconomyhasconvergedtoabalancedgrowthpathwithequalityandtheninsomeperiod,
anarbitrarynodegetsapositiveexogenousshockwhichincreasesitshumancapitalrelative
totherestoftheeconomy.Wepresentthetransitionbacktothebalancedgrowthpathand
ndthatgrowthandinequalityduringthetransitiondependonthepositionoftheshocked
regioninthenetwork.Themorecentralthenodeis,thehigheristheoverallgrowthin
transitionandthelowerinequality.Additionally,asweshocknodeso¤thebalancedgrowth
path,wendthathighgrowthisachievedwhenwemixregionsthataredissimilar(high
disassortativity),andthenetworke¤ectsbecomelarger.Inequalityduringtransitionis
smallerwhenassortativityislow,butthisrelationislessclear.
Finally,weuseschoolandincomedatafromSwitzerlandtoillustratehowourmodel
performsrelativetoamodelthatdoesnotexplicitlytakenetworklinksintoaccount.We
ndthatthereisastrongpositivecorrelationbetweenmodelpredictionsandobserved
data.Importantly,themodelwherethenetworkstructureisexplicitlytakenintoaccount
providesabetterttothedatathanthetwobenchmarkmodelsinwhichweabstractfrom
thenetworkstructurebutallowforgeneralexternalitye¤ects.
Ourpaperisnotthersttoaddresstherelevanceoflocale¤ectsforeconomicgrowthand
inequality.
2
First,Lucas(1988)emphasizedtheroleofexternale¤ectsonhumancapital
accumulationandproductivity.Followingthis,thereisalargenumberofarticlesthat
alsoassumespillovere¤ectsonhumancapitalformation.Forinstance,delaCroixand
Doepke(2003)investigatehowinequalitya¤ectseconomicgrowthinamodelwithfertility
di¤erentials.Thereisalsoanimportantstrandofliteraturethatexaminestheimportance
ofcapitalmarketimperfectionsforhumancapitalformationandthedynamicsofinequality
andgrowth(e.g.GalorandZeira(1993)andBanerjeeandNewman(1993)).Allofthis
literaturegenerallydoesnotmodelnetworkstructuresexplicitly.Morecloselyrelatedtoour
paperistheworkofBénabou(1996)whostudiesasimilarquestiontooursandinvestigates
howsocialcommunitystructurea¤ectsgrowthandinequality.
3
Inhismodel,theacquisition
ofhumancapitalalsoreectstheinuenceoffamily,local(community),andeconomy
widefactors.Last,inamorerecentarticle,Mookherjee,Napel,andRay(2010)emphasize
thatgeographicallocationa¤ectsparentsaspirations.Intheirmodel,whichfeaturesan
2
Ourworkalsobelongstothevastliteraturethatstudiestherelationshipandinteractionsofinequality
andgrowth.AcomprehensivesummaryofthisliteraturecanbefoundinGarcia-PenalosaandTurnovsky
(2006).
3
Inarelatedarticle,Bénabou(1993)showsthatlocalexternalitiesa¤ecttheincentivesofagentsto
segregate,andexaminsthee¤ectsofthisonproductivity.Thismodel,however,isstaticandfocuses
onlocationchoice.Durlauf(1996)alsodemonstrateshowendogenouscommunityformationcangenerate
segregatedsocietiesresultingoninequalitypersistenceandpovertytraps.Ouranalysisisdi¤erent,sincewe
focusontheimpactofdi¤erentnetworkstructuresongrowthandinequality.Weinvestigatewhetherand
underwhatconditionssuchstructurescanbeaprimarycauseofinequalityintheshortandlongrun.
CavalcantiandGiannitsarou
4
exogenouslocation,ahouseholdwillhavehigheraspirations,ifitlivesinaneighborhood
withalargefractionofeducatedneighbors.Again,animportantdi¤erenceofourpaper
tothisliteratureisthatsocialstructuresarerepresentedbyexplicitnetworks.Thismakes
ourframeworkmoretractableandexibleforanalyzingavarietyofnetworksrepresenting
howdi¤erentcommunitiesareinterlinkedandnotonlyfocusingonjusttwoextremetypes
ofsocieties(e.g.,segregatedversusintegrated).
4
Duetothetractabilityofourframework,
weareabletomap
