This document summarizes key points from a lecture on diffusion, identification, and network formation. It discusses how diffusion of products can be modeled, including information passing between neighbors. Estimation techniques are described to model information diffusion on actual networks by simulating propagation over time. The challenges of identification when networks are endogenous are also covered. Forming models of network formation that account for link dependencies is an important area of current research.

1. Lecture'3'
Diffusion,'Iden@fica@on,'
Network'Forma@on'
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Matthew O. Jackson
NBER July 22, 2014
www.stanford.edu~jacksonmJackson-
NBER-slides2014.pdf

2. Lecture'3'
• Diffusion!
• More!on!issues!of!iden<fica<on,!endogeneity!
of!networks,!network!forma<on!

3. Griliches'(1957):'Hybrid'Corn'Diffusion'
S-Shape, Spatial Pattern...
0!
10!
20!
30!
40!
50!
60!
70!
80!
90!
100!
32! 37! 42! 47!
Kentucky!
Wisonsin!
Iowa!
Year!
Frac<on!
Adopted!

4. 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…!

5. 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?!

6. 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,!Garciak
Jimeno,!and!Robinson!!k!rare!…)!
!
• Structural'modeling'of'behavior'(e.g.,'diffusion'model…)'
• Model'network'forma@on...!

7. 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!

8. 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...!

9. Borrow:!

10. Start'with'Standard'Peerh
effects'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!
!!!!!!!!!

11. Start'with'Standard'Peerh
effects'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!
!!!!!!!!!

12. Start'with'Standard'Peerh
effects'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,!!

13. 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!

14. Modeling'behavior/informa@on'
diffusion:'
• Probability!of!passing!to!a!given!individual:!
• qN!!if!did!Not!par<cipate!
• qP!!if!did!Par<cipate!

15. Informa<on!Injec<on!
Not Participate
Participates

16. Passing:!Different!Probabili<es!

17. New!Nodes!Decide!

18. Pass!Again!

19. New!Decisions,!etc.!

20. Choice'Decision'
• Now!condi8onal'upon'being'informed:!
• Log(pi/(1kpi))!!
!!!!!!=!!!b0!!
!!!!!!!!+!bchar!characteris<csi!
!!!!!!!!+!bPeer!!fraci!informing!friends!par<cipa<ng!
!!!!!!!!!

21. 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)!

22. Es<ma<on:!!
qN= .15, qP=.3, b-peer = .5

23. Es<ma<on:!!
qN= .05, qP=.5, b-peer = 1

24. 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]!

25. 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***!

26. 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)!

27. 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!

28. 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

29. 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,!Garciak
Jimeno,!and!Robinson!!k!rare!…)!
!
• Structural'modeling'of'behavior'(e.g.,'diffusion'model…)'
• Model'network'forma@on...!

30. Network'Forma@on'
• Main!challenges!driving!current!literature!
– mul<plicity!!
– integra<ng!forma<on!with!behavior:!
unobservables!
– link!dependencies!!!

31. Ques@ons'
• Always!lurking:!!correlated!unobservables!
• Peoples’!behaviors!correlate!with!network!
posi<on!because!of!homophily!
!

32. Example'
• GoldsmithkPinkham!and!Imbens!(2013)!
!!!!!!!!Yi!=!b0!+!b1Xi!+!b2Y(i)
peer!+!b3X(i)
peer!+!b4Zi!+!ei!
!
!!!!!!!!!!!!!!!!!Zi!!!!!unobserved!characteris<cs!!!!

33. 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!)!

34. 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'''''

35. 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!

36. Link'Dependencies'
• Link!forma<on!is!significantly!correlated!!
• Friends!of!friends!
• Value!to!having!closure!(enforcement!of!
incen<ves...)!

37. 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

38. 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!!!

39. 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)!

40. 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!

41. 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...!

42. 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,!Garciak
Jimeno,!and!Robinson!!k!rare!…)!
!
• Structural!modeling!of!behavior!(e.g.,!diffusion!model…)!
• Model!network!forma<on...!