Jackson nber-slides2014 lecture3

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Jackson nber-slides2014 lecture3

  1. 1. Lecture'3' Diffusion,'Iden@fica@on,' Network'Forma@on' ! ! ! ! ! ! ! Matthew O. Jackson NBER July 22, 2014 www.stanford.edu~jacksonmJackson- NBER-slides2014.pdf
  2. 2. Lecture'3' •  Diffusion! •  More!on!issues!of!iden<fica<on,!endogeneity! of!networks,!network!forma<on!
  3. 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. 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. 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. 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. 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. 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. 9. Borrow:!
  10. 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. 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. 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. 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. 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. 15. Informa<on!Injec<on! Not Participate Participates
  16. 16. Passing:!Different!Probabili<es!
  17. 17. New!Nodes!Decide!
  18. 18. Pass!Again!
  19. 19. New!Decisions,!etc.!
  20. 20. Choice'Decision' •  Now!condi8onal'upon'being'informed:! •  Log(pi/(1kpi))!! !!!!!!=!!!b0!! !!!!!!!!+!bchar!characteris<csi! !!!!!!!!+!bPeer!!fraci!informing!friends!par<cipa<ng! !!!!!!!!!
  21. 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. 22. Es<ma<on:!! qN= .15, qP=.3, b-peer = .5
  23. 23. Es<ma<on:!! qN= .05, qP=.5, b-peer = 1
  24. 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. 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. 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. 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. 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. 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. 30. Network'Forma@on' •  Main!challenges!driving!current!literature! – mul<plicity!! – integra<ng!forma<on!with!behavior:! unobservables! – link!dependencies!!!
  31. 31. Ques@ons' •  Always!lurking:!!correlated!unobservables! •  Peoples’!behaviors!correlate!with!network! posi<on!because!of!homophily! !
  32. 32. Example' •  GoldsmithkPinkham!and!Imbens!(2013)! !!!!!!!!Yi!=!b0!+!b1Xi!+!b2Y(i) peer!+!b3X(i) peer!+!b4Zi!+!ei! ! !!!!!!!!!!!!!!!!!Zi!!!!!unobserved!characteris<cs!!!!
  33. 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. 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. 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. 36. Link'Dependencies' •  Link!forma<on!is!significantly!correlated!! •  Friends!of!friends! •  Value!to!having!closure!(enforcement!of! incen<ves...)!
  37. 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. 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. 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. 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. 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. 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...!

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