Lecture'3'Diffusion,'Iden@fica@on,'Network'Forma@on'

!!!!!!!

Matthew O. Jackson NBER July 22, 2014 www.stanford.edu\~jacksonm\Jackson-NBER-slides2014.pdf

Lecture'3'

•  Diffusion!

•  More!on!issues!of!iden<fica<on,!endogeneity!of!networks,!network!forma<on!

Griliches'(1957):'Hybrid'Corn'Diffusion'

S-Shape, Spatial Pattern...

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10!

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30!

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50!

60!

70!

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90!

100!

32! 37! 42! 47!

Kentucky!

Wisonsin!

Iowa!

Year!

Frac<on!Adopted!

Diffusion'of'a'product/technology'

•  Complementari<es!in!choices/compa<bility!

•  Awareness!–!hear!about!through!friends/acquaintances!

•  Learning!–!about!value!

•  Fads/fashion!

•  Characteris<cs!k!!just!similar!tastes!to!friends!due!to!homophily…!

Dissec@ng'diffusion'

•  Policy!implica<ons!

•  Externali<es!can!cause!diffusion!to!be!too!slow,!inefficient!

•  What!is!driving!diffusion?!!Should!we/can!we!improve!it?!

Iden@fica@on'•  Field/natural!experiments!!(e.g.,!pseudo!random!injec<ons!in!Indian!

data,!iden<fica<on!–!but'don’t'control'networks…)!

•  IV!!!(Just!saw!in!Lecture!2)!–  exploi<ng!network!posi<on!(Bramoulle,!Djebbari,!and!For<n,!!k!does'not'address'endogenous'networks/unobservables…)!!

–  things!that!affect!network,!but!not!behavior!(Acemoglu,!GarciakJimeno,!and!Robinson!!k!rare!…)!

!•  Structural'modeling'of'behavior'(e.g.,'diffusion'model…)'

•  Model'network'forma@on...!

!

Applica@on:'Structural'Modeling'

•  Use!networks!in!richer!way!than!just!mapping!peers!

•  Model!diffusion!and!use!it!to!iden<fy!behavior:!

!!!!Track!paths!of!informa<on!diffusion!

!

Micro'h'Individual'Behavior'and'Peer'Effects:'

•  Disentangling*Peer*effects:*

•  Basic'informa@on'diffusion:'about!a!product!–!being!aware!of!new!product!

•  Peer'influence/Endorsement/Game'on'Network:''even!if!aware,!more!neighbors!taking!ac<on!leads!to!higher!(or!lower)!ac<on!kk!!endorsement!(learning),!peer!pressure,!complementari<es...!

Borrow:!

Start'with'Standard'Peerheffects'analysis:'

Let!pi!be!i’s!choice!of!whether!to!par<cipate!

•  Log(pi/(1kpi))!!!!!!!!=!!!b0!!!!!!!!!!+!bchar!characteris<csi!!!!!!!!!+!bPeer!!fraci!friends!par<cipa<ng!!!!!!!!!!

Start'with'Standard'Peerheffects'analysis:'

Let!pi!be!i’s!choice!of!whether!to!par<cipate!

•  Log(pi/(1kpi))!!!!!!!!=!!!b0!!!!!!!!!!+!bchar!characteris<csi!!!!!!!!!+!2.5***!!fraci!friends!par<cipa<ng!!!!!!!!!!

Start'with'Standard'Peerheffects'analysis:'

Let!pi!be!i’s!choice!of!whether!to!par<cipate!

•  Log(pi/(1kpi))!!!!!!!!=!!!b0!!!!!!!!!!+!bchar!characteris<csi!!!!!!!!!+!2.5***!!fraci!friends!par<cipa<ng!!frac!0!to!1!increases!pi/(1kpi)!by!factor!12.2,!!frac!.1!to!.3!increases!pi/(1kpi)!by!factor!1.65,!!!!!!!!!!!

Modeling'diffusion:'

•  We!know!the!set!of!ini<ally!informed!nodes!

•  Informed!nodes!(repeatedly)!pass!informa<on!randomly!to!their!neighbors!over!discrete!<mes!

•  Once!informed!(just!once),!nodes!choose!to!par<cipate!depending!on!their!characteris<cs!and!their!neighbors’!choices!

Modeling'behavior/informa@on'diffusion:'

•  Probability!of!passing!to!a!given!individual:!•  qN!!if!did!Not!par<cipate!•  qP!!if!did!Par<cipate!

Informa<on!Injec<on!

Not Participate

Participates

Passing:!Different!Probabili<es!

New!Nodes!Decide!

Pass!Again!

New!Decisions,!etc.!

Choice'Decision'

•  Now!condi8onal'upon'being'informed:!

•  Log(pi/(1kpi))!!!!!!!!=!!!b0!!!!!!!!!!+!bchar!characteris<csi!!!!!!!!!+!bPeer!!fraci!informing!friends!par<cipa<ng!!!!!!!!!!

Es@ma@on'technique:'

•  Es<mate!b0,!bchar,!from!ini<ally!informed!(saves!on!computa<on!size!of!grid)!

•  qN,!qP,!bpeer!!k!!For!!each!choice!of!parameters,!simulate!on!the!actual!networks!of!the!villages!for!<me!period!propor<onal!to!number!of!trimesters!in!data!for!village!(3!to!8!<mes)!

•  !Choose!parameters!to!best!match!simulated!par<cipa<on!rates!and!various!moments!to!observed!!moments!(SMM)!

Es<ma<on:!!

qN= .15, qP=.3, b-peer = .5

Es<ma<on:!!

qN= .05, qP=.5, b-peer = 1

Es@mated'parameters:'

•  Informa<on!significant,!peer/endorse!effect!not!

qN! qP! bkpeer! qN!–!qP!Es<mates:! 0.05***! 0.55***! k0.20! k0.50***!

[0.01]! [0.13]! [0.16]! [0.13]!

Es@mated'parameters:'

•  Informa<on!significant,!peer/endorse!effect!not!

qN! qP! bkpeer! qN!–!qP!With!Diffusion! 0.05***! 0.55***! k0.20! k0.50***!

[0.01]! [0.13]! [0.16]! [0.13]!

just!peer:! 2.5***!

Results'from'Fikng'Model'of'Diffusion'in'this'case:'

•  Significant!informa<on!passing!parameters!

•  Insignificant,!limited!Peer!Effects!

•  Informa<on!passing!depends!on!whether!par<cipate:!more!likely!if!par<cipate!

•  Nonpar<cipants!play!a!substan<al!role!(1/3!of!total)!

Broader'Messages:'

•  Simple!network!models!can!help!es8mate'and'dissect!peer!effects!and!diffusion!processes:!!!policy!consequences!

•  Network!structures!have!consequences!for!behavior:!!!!•  Tractable!and!intui<ve!ways!to!quan<fy!despite!complexity!of!networks!

E[d]=20 E[d]=9

E[d]=6

E[d]=3

fraction adopting over time, P(d) = ad-2, Simulated diffusion process, threshold of neighbors

Approaches'•  Field/natural!experiments!!(e.g.,!pseudo!random!injec<ons!in!Indian!

data,!iden<fica<on!–!but'don’t'control'networks…)!

•  IV!!!(Just!saw!in!Lecture!2)!–  exploi<ng!network!posi<on!(Bramoulle,!Djebbari,!and!For<n,!!k!does'not'address'endogenous'networks/unobservables…)!!

–  things!that!affect!network,!but!not!behavior!(Acemoglu,!GarciakJimeno,!and!Robinson!!k!rare!…)!

!•  Structural'modeling'of'behavior'(e.g.,'diffusion'model…)'

•  Model'network'forma@on...!

!

Network'Forma@on'

•  Main!challenges!driving!current!literature!– mul<plicity!!– integra<ng!forma<on!with!behavior:!unobservables!

– link!dependencies!!!

!

Ques@ons'

•  Always!lurking:!!correlated!unobservables!

•  Peoples’!behaviors!correlate!with!network!posi<on!because!of!homophily!

!

Example'

•  GoldsmithkPinkham!and!Imbens!(2013)!

!!!!!!!!Yi!=!b0!+!b1Xi!+!b2Y(i)peer!+!b3X(i)peer!+!b4Zi!+!ei!

!!!!!!!!!!!!!!!!!!Zi!!!!!unobserved!characteris<cs!!!!

Example'

•  U<lity!from!friendship!based!on!homophily:!

!!!!!!!!Ui!(j)!=!a0!+!a1|!Xi!k!Xj!|!+!a2!|!Zi!–!Zj!|+!...!+!eij!!!!!(!...!=!past!network!rela<onships!if!available,!!!!!!!!!!!!!!!!e.g.,!past!friends!in!common,!!linked!in!past!)!

Es@mate'Unobservables'!!!!!Yi!=!b0!+!b1Xi!+!b2Y(i)peer!+!b3X(i)peer!+!b4Zi!+!ei!!!!!!!!!!Ui!(j)!=!a0!+!a1|!Xi!k!Xj!|!+!a2!|!Zi!–!Zj!|+!...!+!eij!

Links!logis<c!in!Ui!(j)!,!Uj!(i)!!Es<mate!system!(Bayesian,!MLE)!!!!Infer'unobservable'Zi’s'':'''''ij'connected'with'distant'Xi’s'have'similar'Zi’s''''ij''unlinked'with'similar'Xi’s'have'differing'Zi’s'''''

Lesson:'

Yi = b0 + b1Xi + b2Y(i)

peer + b3X(i)peer + b4Zi + ei !

•  Accoun<ng!for!link!forma<on!can!help!infer!unobservables!

•  Can!help!correct!es<mates!of!strategic!interac<on!with!friends/acquaintances!

Link'Dependencies'

•  Link!forma<on!is!significantly!correlated!!

•  Friends!of!friends!

•  Value!to!having!closure!(enforcement!of!incen<ves...)!

Link!Dependencies!k!Clustering!Coefficients:!

•  Prison!friendships!!!!•  .31!(MacRae!60)!vs!.0134!

•  Cokauthorships!•  .15!math!(Grossman!02)!vs!.00002,!!!•  .09!biology!(Newman!01)!vs!.00001,!!•  .19!econ!(Goyal,!van!der!Leij,!Moraga!06)!vs!.00002,!

•  Floren<ne!Marriage!and!Business!dealings!!!•  .46!on!15!central!families!!!!vs!!.29...!

Freq of this link?

1 2

3

Challenges'

•  No!longer!talk!about!probabili<es!at!link!level!

•  But!cannot!calculate!probabili<es!at!network!level:!!!too!many!networks!to!do!MLE/Bayesian!calcula<ons!!!

Models'of'Network'Forma@on'with'Dependencies'

•  Dynamic/Specific!Models!(JacksonkWolinsky!96,!BarabasikAlbert!99,!BalakGoyal!00,!JacksonkWa_s!00,!JacksonkRogers!07,!CurrarinikJacksonkPin!09,10,!Christakis!et!al.!10,!Bramoulle!et!al.!12,!Mele!12…)!!

•  ERGMs!!(FrankkStrauss!86,!WassermankPa|son!96,!Snjiders!02,!Handcock!03...)!es<ma<on!problems!!

•  Subgraphs,!probabili<es!of!seeing!specific!configura<ons!of!links!(ChandrasekharkJackson!13)!

!

Broader'Messages:'

•  Simple!network!models!can!help!es8mate'and'dissect!peer!effects!and!diffusion!processes:!!!policy!consequences!

•  Network!structures!have!consequences!for!behavior:!!!!•  Tractable!and!intui<ve!ways!to!quan<fy!despite!complexity!of!networks!

Simplifying'the'Complexity'•  Global!pa_erns!of!networks!

– path!lengths!– degree!distribu<ons...!

•  Segrega<on!Pa_erns:!node!types!and!homophily!•  Local!Pa_erns!

– Clustering!– Support…!

•  Posi<ons!in!networks!– neighborhoods!– Centrality,!!influence...!

Iden@fica@on'•  Field/natural!experiments!!(e.g.,!pseudo!random!injec<ons!in!Indian!

data,!iden<fica<on!–!but'don’t'control'networks…)!

•  IV!!!(Just!saw!in!Lecture!2)!–  exploi<ng!network!posi<on!(Bramoulle,!Djebbari,!and!For<n,!!k!does'not'address'endogenous'networks/unobservables…)!!

–  things!that!affect!network,!but!not!behavior!(Acemoglu,!GarciakJimeno,!and!Robinson!!k!rare!…)!

!•  Structural!modeling!of!behavior!(e.g.,!diffusion!model…)!

•  Model!network!forma<on...!

!