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The Old Boy (and Girl) Network: Social Network Formation on University Campuses. Adi Mayer and Steve Puller Texas A&M. Motivation to Study Social Networks in Higher Education. Social networks determine “peer effects” in college - PowerPoint PPT Presentation
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The Old Boy (and Girl) Network: The Old Boy (and Girl) Network:
Social Network Formation Social Network Formation
on University Campuseson University Campuses
Adi Mayer and Steve PullerAdi Mayer and Steve Puller
Texas A&MTexas A&M
Motivation to StudyMotivation to Study Social Networks in Higher Education Social Networks in Higher Education
Social networks determine “peer effects” Social networks determine “peer effects” in collegein college
Sacerdote (2001), Zimmerman (2003), Winston and Sacerdote (2001), Zimmerman (2003), Winston and Zimmerman (2003), Kremer and Levy (2003), Stinebrickner Zimmerman (2003), Kremer and Levy (2003), Stinebrickner & Stinebrickner (2005), …& Stinebrickner (2005), …
Does race affect social interaction / are Does race affect social interaction / are universities “really” integrated?universities “really” integrated?
Sacerdote & Marmaros (2006)Sacerdote & Marmaros (2006)
Information transmissionInformation transmission Granovetter’s “Strength of Weak Ties”Granovetter’s “Strength of Weak Ties”
Motivation: Motivation: Role of Social Networks in Labor Role of Social Networks in Labor
MarketMarket Social Connections are important for job search:Social Connections are important for job search:
““While the frequency of alternative job-finding methods While the frequency of alternative job-finding methods varies somewhat by sex and occupation, the following varies somewhat by sex and occupation, the following generalization seems fair: generalization seems fair: approximately approximately 50%50% of all of all workers currently employed found their jobs workers currently employed found their jobs through friends and relativesthrough friends and relatives” ” (Montgomery 1991)(Montgomery 1991)
Determination of Wages / EmploymentDetermination of Wages / Employment Job search through social networks generates:Job search through social networks generates:
positively correlated employment across agents and positively correlated employment across agents and time time
positive duration dependence of unemploymentpositive duration dependence of unemployment social networks can generate inequality between two social networks can generate inequality between two
otherwise equivalent groupsotherwise equivalent groups
Calvo-Armengol and Jackson (2004), Pellizarri (2004), Ioannides and Calvo-Armengol and Jackson (2004), Pellizarri (2004), Ioannides and Soetevent (2006), Arrow and Borzekowski (2004)Soetevent (2006), Arrow and Borzekowski (2004)
1) Document structure and segmentation in social network at 10 universities
For one university:
2) Reduced-form description of factors that predict social connections between any two students
3) Explicit model of network formation with counterfactual experiments
Empirical Approach In This Paper:Empirical Approach In This Paper:
What determines the formation of What determines the formation of social networks?social networks?
Social network
Preferences / Tastes
Environment
Do individuals want to be friends?
Do individuals have contact?
What determines the formation of What determines the formation of social networks?social networks?
Social network
Preferences / Taste Environment
•Race
•Parental background
•Political orientation
•Abilities
•Composition of student body
•Curriculum
•Dorm assignment
•Clubs / Activities
What determines the formation of What determines the formation of social networks?social networks?
Social network
Preferences / Taste Environment
•Race
•Parental background
•Political orientation
•Abilities
•Composition of student body
•Curriculum
•Dorm assignment
•Clubs / Activities
Policy Instrume
nts
Model of Network formationModel of Network formation
Simulate NetworkSimulate Network
Stage 1: Students meet with probability varying in institutional Stage 1: Students meet with probability varying in institutional
features (e.g. same dorm)features (e.g. same dorm)
Stage 2: Conditional upon meeting, students form friendships Stage 2: Conditional upon meeting, students form friendships
based upon tastes for observable characteristicsbased upon tastes for observable characteristics
Stage 3: Students meet friends of friends with some probability, Stage 3: Students meet friends of friends with some probability,
and again may form friendshipsand again may form friendships
Calibrate parameters of model so simulated network resembles actual Calibrate parameters of model so simulated network resembles actual
networknetwork
Perform Counterfactual ExperimentsPerform Counterfactual Experiments
““Turn off” institutional effects and make all meeting randomTurn off” institutional effects and make all meeting random
““Turn off” tastes and make all “liking” randomTurn off” tastes and make all “liking” random
X-Percent Rule – add more students with specific characteristicsX-Percent Rule – add more students with specific characteristics
Policy
Instruments
Preferences
Preview of ResultsPreview of Results
University social networks exhibit standard features University social networks exhibit standard features
of social networksof social networks
E.g. ClusteringE.g. Clustering
Networks exhibit only modest segmentation in some Networks exhibit only modest segmentation in some
dimensions (ability, parental education, political dimensions (ability, parental education, political
orientation), but substantial segmentation by raceorientation), but substantial segmentation by race
University policies have very limited ability to University policies have very limited ability to
reduce segmentation by racereduce segmentation by race
DataData
From facebook.comFrom facebook.com 10 universities in Texas10 universities in Texas
Texas A&M registrarTexas A&M registrar Additional administrative dataAdditional administrative data
www.facebook.comwww.facebook.com
Online student social network directory for Online student social network directory for each universityeach university
Need official University e-mail to sign upNeed official University e-mail to sign up
Started on February 4, 2004 at HarvardStarted on February 4, 2004 at Harvard
By July 2006, 7By July 2006, 7thth most visited website in US most visited website in US
DataData From facebook.comFrom facebook.com
All student profiles as of 1/17/05 for 10 universities in All student profiles as of 1/17/05 for 10 universities in TexasTexas
65,104 undergraduates65,104 undergraduates (Self-reported) Demographics: year, birthdate, gender, (Self-reported) Demographics: year, birthdate, gender,
high school, hometown, major, current courses, dating high school, hometown, major, current courses, dating status, residence hall, political orientation, jobs, hobbiesstatus, residence hall, political orientation, jobs, hobbies
Social network: links to friends at own-school & other Social network: links to friends at own-school & other schools schools
Race – we classify based upon picturesRace – we classify based upon pictures
Texas A&M registrar:Texas A&M registrar: Race, College performance (GPA), High school Race, College performance (GPA), High school
performance (SAT, class rank), Parental characteristics performance (SAT, class rank), Parental characteristics (income, parents’ education), College activities(income, parents’ education), College activities
The 10 UniversitiesThe 10 Universities
UniversityUniversityUndergradUndergrad EnrollmentEnrollment
FacebookFacebooksamplesample
Fraction in Fraction in FacebookFacebook
RiceRice 2,9332,933 2,3542,354 0.800.80
U TexasU Texas 36,47336,473 14,72814,728 0.400.40
Texas A&MTexas A&M 35,60535,605 15,79715,797 0.440.44
BaylorBaylor 11,52111,521 7,0087,008 0.610.61
Texas TechTexas Tech 23,32923,329 7,2197,219 0.310.31
Texas ChristianTexas Christian 7,0247,024 3,6783,678 0.520.52
SMUSMU 6,0906,090 3,4963,496 0.570.57
U North TexasU North Texas 24,27424,274 4,4744,474 0.180.18
UT ArlingtonUT Arlington 18,17618,176 1,4421,442 0.080.08
Texas StateTexas State 22,40222,402 4,9084,908 0.220.22
Texas A&MTexas A&MStudents In Students In FacebookFacebook
Overall Overall Student Student
PopulationPopulation
GPRGPR 2.952.95 2.932.93
SATSAT 11681168 11521152
High School %ile Class RankHigh School %ile Class Rank 86.586.5 86.086.0
Texas ResidentTexas Resident 97.4%97.4% 97.4%97.4%
FemaleFemale 55.2%55.2% 50.6%50.6%
In a GreekIn a Greek 14.3%14.3% 11.6%11.6%
Lives in a dormLives in a dorm 41.1%41.1% 33.7%33.7%
AthleteAthlete 2.5%2.5% 2.5%2.5%
FreshmanFreshman 27%27% 22%22%
SophomoreSophomore 27%27% 22%22%
JuniorJunior 26%26% 26%26%
SeniorSenior 20%20% 29%29%
WhiteWhite 81.8%81.8% 80.5%80.5%
HispanicHispanic 11.4%11.4% 12.0%12.0%
AsianAsian 4.0%4.0% 3.8%3.8%
BlackBlack 2.3%2.3% 2.9%2.9%
Father College DegreeFather College Degree 61%61% 58%58%
Mother College DegreeMother College Degree 54%54% 51%51%
Household Income < $40,000Household Income < $40,000 14%14% 17%17%
Household Income > $80,000Household Income > $80,000 53%53% 48%48%
Segmentation by Race (Table 5)Segmentation by Race (Table 5) Relative probability of friendship Relative probability of friendship
Pair of:Pair of: RiceRice BaylorBaylorTexasTexasA&MA&M U TexasU Texas
White/Hisp & White/HWhite/Hisp & White/H 1.031.03 1.101.10 1.011.01 1.121.12
White/Hisp & AsianWhite/Hisp & Asian 0.790.79 0.430.43 0.740.74 0.420.42
White/Hisp & BlackWhite/Hisp & Black 0.870.87 0.410.41 0.770.77 0.560.56
Asian & AsianAsian & Asian 2.412.41 4.244.24 7.427.42 4.134.13
Asian & BlackAsian & Black 0.920.92 0.520.52 1.011.01 0.540.54
Black & BlackBlack & Black 5.125.12 5.995.99 16.5416.54 13.1313.13
Any two studentsAny two students 11 11 11 11
Number of pairs of blacks who are friends
Total number of pairs of blacksRelative Probability of Friendship (black&black) = .
Number of pairs of any students who are friends
Total number of any pairs
RiceRice BaylorBaylorTexas Texas A&MA&M U TexasU Texas
Fraction of Students White/HispFraction of Students White/Hisp 0.820.82 0.910.91 0.960.96 0.850.85
Fraction Friends of Whites/Hisp who are Fraction Friends of Whites/Hisp who are White/HispWhite/Hisp 0.850.85 0.960.96 0.970.97 0.930.93
Fraction of Students AsianFraction of Students Asian 0.130.13 0.030.03 0.020.02 0.130.13
Fraction Friends of Asians who are AsianFraction Friends of Asians who are Asian 0.300.30 0.250.25 0.160.16 0.580.58
Fraction of Students BlackFraction of Students Black 0.050.05 0.060.06 0.020.02 0.020.02
Fraction Friends of Blacks who are BlackFraction Friends of Blacks who are Black 0.250.25 0.470.47 0.270.27 0.380.38
Fraction black friends of black student
Relative Probability of Friendship (black&black) * (share of blacks in population)
Segmentation by Race (Table 5)Segmentation by Race (Table 5) “Absolute” Segmentation “Absolute” Segmentation
Segmentation by Political Segmentation by Political Orientation (Table 6)Orientation (Table 6)
RiceRice BaylorBaylorTexas Texas A&MA&M
U U TexasTexas
Fraction of Students LiberalFraction of Students Liberal 0.320.32 0.080.08 0.060.06 0.230.23
Fraction Friends of Lib. who are Lib.Fraction Friends of Lib. who are Lib. 0.380.38 0.120.12 0.100.10 0.290.29
Fraction of Students ConservativeFraction of Students Conservative 0.150.15 0.470.47 0.540.54 0.230.23
Fraction Fraction FriendsFriends of Cons. who are Cons.of Cons. who are Cons. 0.210.21 0.580.58 0.630.63 0.390.39
Pair of:Pair of: Relative probability of friendship Relative probability of friendship
Liberal & LiberalLiberal & Liberal 1.221.22 1.131.13 1.281.28 1.061.06
Liberal & ConservativeLiberal & Conservative 0.860.86 0.590.59 0.690.69 0.750.75
Conservative & ConservativeConservative & Conservative 1.351.35 1.411.41 1.281.28 2.172.17
Any two studentsAny two students 11 11 11 11
Segmentation by Major (Table 6)Segmentation by Major (Table 6)
RiceRice BaylorBaylorTexas Texas A&MA&M U TexasU Texas
Fraction of Students in Same Major Fraction of Students in Same Major if Friends Randomif Friends Random 0.040.04 0.020.02 0.020.02 0.020.02
Fraction of Students in Same MajorFraction of Students in Same Major 0.080.08 0.060.06 0.070.07 0.080.08
Structure of Networks (Table 3)Structure of Networks (Table 3)
RiceRice BaylorBaylorTexas Texas A&MA&M U TexasU Texas
Avg. Number of FriendsAvg. Number of Friends 50.850.8 59.859.8 41.141.1 39.539.5
Variance of # FriendsVariance of # Friends 31.931.9 50.850.8 38.438.4 36.536.5
Skewness of # FriendsSkewness of # Friends 1.061.06 1.741.74 2.062.06 2.012.01
Cluster CoefficientCluster Coefficient 0.240.24 0.190.19 0.170.17 0.200.20
Cluster Coefficient ConservativesCluster Coefficient Conservatives 0.280.28 0.210.21 0.180.18 0.240.24
Cluster Coefficient LiberalsCluster Coefficient Liberals 0.240.24 0.160.16 0.140.14 0.190.19
Cluster Coefficient BlacksCluster Coefficient Blacks 0.440.44 0.300.30 0.320.32 0.370.37
Cluster Coefficient AsiansCluster Coefficient Asians 0.310.31 0.300.30 0.260.26 0.250.25
Avg. Degrees of SeparationAvg. Degrees of Separation 2.302.30 2.622.62 2.952.95 3.003.00
Rest of Paper: Texas A&M Rest of Paper: Texas A&M onlyonly
, , for all ij i j ijFriends f X X i j
7,719 students
N*(N-1)/2 = 29,787,621 pairs
0.34 % of all pairs are friends
Linear probability modelLinear probability model
Sample: All pairs of students in facebook that are matched to TAMU records and we observe all
characteristics.
Linear probability modelLinear probability model
Regress Friends Y/N onRegress Friends Y/N on
Race (e.g. White-White, White-Black, etc.)Race (e.g. White-White, White-Black, etc.) High School, Cohort, GenderHigh School, Cohort, Gender Family BackgroundFamily Background Dorm, AcademicDorm, Academic AbilityAbility ActivitiesActivities
Predictors of friendship (Table 8)Predictors of friendship (Table 8)
RR22
RaceRace 0.00060.0006
High School, Age, High School, Age, GenderGender 0.02930.0293
Family BackgroundFamily Background 0.00010.0001
Dorm, AcademicDorm, Academic 0.00330.0033
AbilityAbility 0.00010.0001
ActivitiesActivities 0.00320.0032
All CovariatesAll Covariates 0.03600.0360
Predictors of friendship:Predictors of friendship: Dorm /AcademicsDorm /Academics
Only Only Dorm, AcademicDorm, Academic All CovariatesAll Covariates
CoefCoef CoefCoef
ConstantConstant 0.0028*0.0028* 0.0028*0.0028*
Same DormSame Dorm 0.0426*0.0426* 0.0407*0.0407*
Same MajorSame Major 0.0038*0.0038* 0.0030*0.0030*
Same College Same College 0.0018*0.0018* 0.0016*0.0016*
R2= 0.0033
Predictors of friendship: Predictors of friendship: ActivitiesActivities
Only activitiesOnly activities All CovariatesAll Covariates
CoefCoef CoefCoef
ConstantConstant 0.0030*0.0030* 0.0028*0.0028*
Both are AthletesBoth are Athletes 0.0649*0.0649* 0.0635*0.0635*
Both in Corps of CadetsBoth in Corps of Cadets 0.0536*0.0536* 0.0428*0.0428*
Both are GreekBoth are Greek 0.0192*0.0192* 0.0188*0.0188*
One is GreekOne is Greek -0.0003*-0.0003* -0.0003*-0.0003*
One is AthleteOne is Athlete -0.0003-0.0003 -0.0003-0.0003
One in Corps of CadetsOne in Corps of Cadets -0.0005-0.0005 -0.0004-0.0004
R2= 0.0032
Predictors of friendship: Predictors of friendship: RaceRace
Only RaceOnly Race All CovariatesAll Covariates
CoefficientCoefficient CoefficientCoefficient
ConstantConstant 0.0026*0.0026* 0.0028*0.0028*
Both BlackBoth Black 0.0562*0.0562* 0.0542*0.0542*
Both AsianBoth Asian 0.0132*0.0132* 0.0126*0.0126*
Both HispanicBoth Hispanic 0.0028*0.0028* 0.0027*0.0027*
Hispanic - BlackHispanic - Black 0.00110.0011 0.00100.0010
Both WhiteBoth White 0.0011*0.0011* 0.00090.0009
Asian - BlackAsian - Black 0.00080.0008 0.00100.0010
Hispanic - AsianHispanic - Asian 0.00020.0002 0.00050.0005
White - HispanicWhite - Hispanic 0.00010.0001 0.00030.0003
White - BlackWhite - Black -0.0001-0.0001 -0.0002-0.0002
White - AsianWhite - Asian -0.0002-0.0002 -0.0002-0.0002R2= 0.0006
Baseline Probability of friendship = 0.34 percentBaseline Probability of friendship = 0.34 percent
Effect of common friends? (Table Effect of common friends? (Table 9)9)
# of common friends# of common friends ---- 0.0298*0.0298*
ConstantConstant 0.0028*0.0028* -0.0003-0.0003
Both BlackBoth Black 0.0542*0.0542* 0.0151*0.0151*
Both AsianBoth Asian 0.0126*0.0126* 0.0071*0.0071*
Both HispanicBoth Hispanic 0.0027*0.0027* 0.0013*0.0013*
Same High SchoolSame High School 0.1859*0.1859* 0.1379*0.1379*
Same Year in CollegeSame Year in College 0.0010*0.0010* 0.0012*0.0012*
Same GenderSame Gender 0.00000.0000 -0.0005*-0.0005*
Same DormSame Dorm 0.0407*0.0407* 0.0214*0.0214*
Same MajorSame Major 0.0030*0.0030* 0.0024*0.0024*
Both are AthletesBoth are Athletes 0.0635*0.0635* 0.0111*0.0111*
Both are GreekBoth are Greek 0.0188*0.0188* -0.0083*-0.0083*
RR22 0.03600.0360 0.24560.2456Note: all covariates included but not reportedNote: all covariates included but not reported
Endogenous effects through friends of friendsEndogenous effects through friends of friends
Friends of friends matterFriends of friends matter
Magnification of exogenous network Magnification of exogenous network determinatesdeterminates
Simple prediction based on reduced Simple prediction based on reduced from estimation misleadingfrom estimation misleading
Model network formationModel network formation
A model of network formationA model of network formation
• Understand process and Understand process and determinants determinants .. of network of network formationformation
- Meeting vs. TasteMeeting vs. Taste
- Friends of friendsFriends of friends
• Generate counterfactualsGenerate counterfactuals
• Policy evaluationPolicy evaluation
A model of network formationA model of network formation
Random Graph Theory Random Graph Theory - cannot explain network features like clusteredness- cannot explain network features like clusteredness
Jackson & Rogers (2005)Jackson & Rogers (2005) Random Meeting & SearchRandom Meeting & Search
- Generates network features- Generates network features- No preferences- No preferences- No institutions / environmental differences - No institutions / environmental differences
We add: We add: (1) environmental differences (1) environmental differences
(2) preferences that determine friendship (2) preferences that determine friendship conditional on conditional on meeting meeting
A model of network formationA model of network formation
Observe features of real networkObserve features of real network
Simulate network model for set of parametersSimulate network model for set of parameters
Calculate features of simulated network Calculate features of simulated network
Pick parameters so that features of simulated Pick parameters so that features of simulated
and actual network are as similar as possibleand actual network are as similar as possible
Graph Theoretic Description of Graph Theoretic Description of NetworkNetwork
nn students students
gg is is nn x x nn friendship matrixfriendship matrix
iff iff i,ji,j are friends are friends
otherwiseotherwise
( , ) 1g i j
( , ) 0g i j
Network formationNetwork formation
Initially Initially g=0g=0
1) Meet random students1) Meet random students Like each other? Like each other?
Yes => Yes => ggijij=1=1
2) Meet students in same 2) Meet students in same environmentenvironment Like each other?Like each other?
Yes => Yes => ggijij=1=1
3) Meet friends of friends3) Meet friends of friends Like each other?Like each other?
Yes => Yes => ggijij=1=1
1) Random
3) Fr of Fr
2) Environment
Network formationNetwork formation
Random MeetingRandom Meeting
Each student meets each other student with probabilityEach student meets each other student with probability ppinitinit
Meet students from same environmentMeet students from same environment
• Meet other students in same college with probability Meet other students in same college with probability ppicollicoll • Each student in same cohort with probability Each student in same cohort with probability ppYEARYEAR
• Each other student in same dorm with probability Each other student in same dorm with probability ppDORMDORM
Meet friends of friendsMeet friends of friends
• Each student Each student ii meets all friends of their friends ( meets all friends of their friends (ggikik=1 and =1 and ggkjkj=1) =1)
with probability with probability ppfrofrfrofr
• Repeated Repeated SS times times
Network formationNetwork formation
Friendship formation conditional on meetingFriendship formation conditional on meeting
• Two students who met become friends if:Two students who met become friends if:
g(i,j)g(i,j) = = II(U(Uijij(.) (.) ≥≥ c cii)·)· I I (U (Ujiji (.) (.)≥ ≥ ccjj))
≡ ≡ II ( ( f f ((XXii,,XXjj,,uuijij;β ;β ) > 0) ) > 0)
where where UUijij = utility to = utility to ii of being friends with of being friends with jj
cci = marginal cost of friendship to = marginal cost of friendship to student student ii
XX = = observable characteristics observable characteristics u =u = unobservable characteristics unobservable characteristics
Network formationNetwork formation
Two students i,j who met become friends if: , , 0 i j ijf X X u
0
_
, ,
_ _ _
1
1200
i j ij
WW i j BB i j
HH i j AA i j
par edu i j
cons i i
skill i
f X X u
I race race white I race race black
I race race hispanic I race race asian
I parent edu parent edu both coll
I conservative conservative
I SAT
& 1200j ijSAT u
Key AssumptionsKey Assumptions Unobserved tastes are uncorrelated with Unobserved tastes are uncorrelated with
institutional meeting channelsinstitutional meeting channels e.g. No taste for other engineering majorse.g. No taste for other engineering majors
Unobserved determinants of meeting are Unobserved determinants of meeting are uncorrelated with observable taste characteristicsuncorrelated with observable taste characteristics e.g. No Black/Hispanic Student Associatione.g. No Black/Hispanic Student Association
Assessing validity from reduced-form regressions:Assessing validity from reduced-form regressions: Coefficients of College/Cohort/Dorm are robust to Coefficients of College/Cohort/Dorm are robust to
inclusion of covariates on Race/Family inclusion of covariates on Race/Family Background/AbilityBackground/Ability
Coefficients of Race/Family Background/Ability are Coefficients of Race/Family Background/Ability are robust to inclusion of College/Cohort/Dormrobust to inclusion of College/Cohort/Dorm
Model FitModel Fit
Moments Entering CalibrationSample of 1930
StudentsFull Model Simulation
Average # of Friends 6.42 6.42
Variance of # of Friends 6.44 6.27
Skewness of # of Friends 1.82 1.82
Cluster Coefficient 0.15 0.16
Fraction from Same Year 0.44 0.44
Fraction from Same College 0.22 0.22
Fraction from Same Dorm 0.08 0.07
Fraction White Friends of Whites 0.87 0.85
Fraction Hispanic Friends of Hispanics 0.21 0.22
Fraction Asian Friends of Asians 0.15 0.14
Fraction Black Friends of Blacks 0.32 0.33
Fraction Hi SAT Score Friends of Hi SAT 0.49 0.49
Fraction Friends of Same Parental Education 0.53 0.53
Fraction Conservative Friends of Conservative 0.62 0.62
Counterfactual ExperimentsCounterfactual Experiments
Simulate Simulate counterfactual counterfactual network changing…network changing… Institutions that affect Institutions that affect
meeting probabilitymeeting probability Preferences for Preferences for
friends with specific friends with specific characteristicscharacteristics
Friend of friends Friend of friends meeting channelmeeting channel
Random
Fr of Fr
Instit.
Counterfactual ExperimentsCounterfactual Experiments
Simulate Simulate counterfactual counterfactual network changing…network changing… Institutions that Institutions that
affect meeting affect meeting probabilityprobability
Preferences for friends Preferences for friends with specific with specific characteristicscharacteristics
Friend of friends Friend of friends meeting channelmeeting channel
Random
Fr of Fr
Instit.
Counterfactual ExperimentsCounterfactual Experiments
Simulate Simulate counterfactual counterfactual network changing…network changing… Institutions that affect Institutions that affect
meeting probabilitymeeting probability Preferences for Preferences for
friends with specific friends with specific characteristicscharacteristics
Friend of friends Friend of friends meeting channelmeeting channel
Random
Fr of Fr
Instit.
Counterfactual ExperimentsCounterfactual Experiments
Simulate Simulate counterfactual counterfactual network changing…network changing… Institutions that affect Institutions that affect
meeting probabilitymeeting probability Preferences for Preferences for
friends with specific friends with specific characteristicscharacteristics
Friend of friends Friend of friends meeting channelmeeting channel
Random
Fr of Fr
Instit.
Counterfactuals: Counterfactuals: MeetingMeeting
Random
Fr of Fr
Instit.
Random
Fr of Fr
Instit.
Moments Entering CalibrationFull Model Simulation
Completely Random Friends
Full Model without
friends of friends
Random Meeting
Average # of Friends 6.42 6.41 6.42 6.41
Variance of # of Friends 6.27 2.52 2.96 5.56
Skewness of # of Friends 1.82 0.39 0.69 1.58
Cluster Coefficient 0.16 0.00 0.01 0.17
Fraction from Same Year 0.44 0.25 0.59 0.25
Fraction from Same College 0.22 0.13 0.31 0.13
Fraction from Same Dorm 0.07 0.01 0.14 0.01
Fraction White Friends of Whites 0.85 0.82 0.85 0.85
Fraction Hispanic Friends of Hispanics 0.22 0.12 0.23 0.22
Fraction Asian Friends of Asians 0.14 0.04 0.14 0.14
Fraction Black Friends of Blacks 0.33 0.02 0.22 0.28
Fraction Hi SAT Score Friends of Hi SAT 0.49 0.39 0.47 0.47
Fraction Friends of Same Parental Edu 0.53 0.44 0.50 0.52
Fraction Conservative Friends of Cons. 0.62 0.52 0.59 0.61
Random
Fr of Fr
Instit.Random
Fr of Fr
Instit.
Counterfactuals: PreferencesCounterfactuals: PreferencesRandom
Fr of Fr
Instit.
Moments Entering CalibrationFull Model Simulation
Random Meeting
No Preferences
Average # of Friends 6.42 6.41 6.42
Variance of # of Friends 6.27 5.56 5.77
Skewness of # of Friends 1.82 1.58 1.56
Cluster Coefficient 0.16 0.17 0.16
Fraction from Same Year 0.44 0.25 0.44
Fraction from Same College 0.22 0.13 0.21
Fraction from Same Dorm 0.07 0.01 0.07
Fraction White Friends of Whites 0.85 0.85 0.82
Fraction Hispanic Friends of Hispanics 0.22 0.22 0.12
Fraction Asian Friends of Asians 0.14 0.14 0.03
Fraction Black Friends of Blacks 0.33 0.28 0.02
Fraction Hi SAT Score Friends of Hi SAT 0.49 0.47 0.41
Fraction Friends of Same Parental Education 0.53 0.52 0.45
Fraction Conservative Friends of Conservative 0.62 0.61 0.53
Random
Fr of Fr
Instit. Random
Fr of Fr
Instit.
Counterfactuals: Double Hispanic StudentsCounterfactuals: Double Hispanic Students
Moments Entering CalibrationFull Model Simulation
Completely Random Friends
Affirmative Action, double
hispanics
Average # of Friends 6.42 6.41 6.41
Variance of # of Friends 6.27 2.52 6.40
Skewness of # of Friends 1.82 0.39 1.88
Cluster Coefficient 0.16 0.00 0.16
Fraction from Same Year 0.44 0.25 0.45
Fraction from Same College 0.22 0.13 0.21
Fraction from Same Dorm 0.07 0.01 0.08
Fraction White Friends of Whites 0.85 0.82 0.76
Fraction Hispanic Friends of Hispanics 0.22 0.12 0.42
Fraction Asian Friends of Asians 0.14 0.04 0.12
Fraction Black Friends of Blacks 0.33 0.02 0.28
Fraction Hi SAT Score Friends of Hi SAT 0.49 0.39 0.47
Fraction Friends of Same Parental Education 0.53 0.44 0.50
Fraction Conservative Friends of Conservative 0.62 0.52 0.60
Counterfactuals: Introduction to MinoritiesCounterfactuals: Introduction to Minorities
Moments Entering CalibrationFull Model Simulation
Completely Random Friends
Introduction to students of different race
Average # of Friends 6.42 6.41 6.41
Variance of # of Friends 6.27 2.52 6.14
Skewness of # of Friends 1.82 0.39 1.79
Cluster Coefficient 0.16 0.00 0.17
Fraction from Same Year 0.44 0.25 0.39
Fraction from Same College 0.22 0.13 0.20
Fraction from Sam Dorm 0.07 0.01 0.06
Fraction White Friends of Whites 0.85 0.82 0.77
Fraction Hispanic Friends of Hispanics 0.22 0.12 0.21
Fraction Asian Friends of Asians 0.14 0.04 0.14
Fraction Black Friends of Blacks 0.33 0.02 0.31
Fraction Hi SAT Score Friends of Hi SAT 0.49 0.39 0.48
Fraction Friends of Same Parental Education 0.53 0.44 0.51
Fraction Conservative Friends of Conservative 0.62 0.52 0.60
Policy = introduce each white to 1% of minorities Policy = introduce each white to 1% of minorities and each minority to 1% of whitesand each minority to 1% of whites
CounterfactualsCounterfactuals Environment has little influence on Environment has little influence on
segmentation by race, ability, backgroundsegmentation by race, ability, background
Affirmative action increases absolute Affirmative action increases absolute segregation of minority, but exposes more segregation of minority, but exposes more white students to minority studentswhite students to minority students
Introduction - small effect on absolute Introduction - small effect on absolute segregation, increases exposure of whites segregation, increases exposure of whites to minority students.to minority students.
ConclusionConclusion
Social networks at universities are Social networks at universities are
segmentedsegmented
Social networks at universities exhibit Social networks at universities exhibit
classic characteristicsclassic characteristics
Limited potential for policies that make Limited potential for policies that make
encounters more randomencounters more random
Other Future Research PossibilitiesOther Future Research Possibilities
Measure “peer effects” on educational Measure “peer effects” on educational outcomesoutcomes Grades (data for TAMU)Grades (data for TAMU) First jobs (TAMU students report at graduation)First jobs (TAMU students report at graduation)
Peer effects in high schoolPeer effects in high school Analyze effects of “school splits” along Analyze effects of “school splits” along
socioeconomic lines on social integrationsocioeconomic lines on social integration Effect of random college/dorm assignment Effect of random college/dorm assignment
at Riceat Rice Field experiment – measure transmission Field experiment – measure transmission
of information through network by of information through network by disseminating job adsdisseminating job ads
THE ENDTHE END
Network FeaturesNetwork Features
ClusterednessClusteredness
Are the friends of your friends also your Are the friends of your friends also your friends?friends?
: , ,
: , ,
ij jk iki j i k j i
iij jk
i j i k j i
g g g
Clustercoefficientg g
Predictors of friendship:Predictors of friendship: High-school / AgeHigh-school / Age
OnlyOnlyHigh School, AgeHigh School, Age All CovariatesAll Covariates
Coef.Coef. Coef.Coef.
ConstantConstant 0.00390.0039 0.00280.0028
Same High SchoolSame High School 0.18640.1864 0.18590.1859
Same GenderSame Gender 0.00060.0006 0.00000.0000
Same Year in CollegeSame Year in College 0.00100.0010 0.00100.0010
Difference b/t Yrs in CollegeDifference b/t Yrs in College -0.0013-0.0013 -0.0011-0.0011
R2= 0.0293
Predictors of friendship: Predictors of friendship: BackgroundBackground
Only Only Family Family
BackgroundBackground All CovariatesAll Covariates
CoefCoef CoefCoef
ConstantConstant 0.00270.0027 0.00280.0028
Both from High Income HouseholdsBoth from High Income Households 0.00060.0006 0.00020.0002
Both from Low Income HouseholdsBoth from Low Income Households 0.00020.0002 0.00020.0002
2 College Parents - 2 College Parents2 College Parents - 2 College Parents 0.00140.0014 0.00090.0009
2 College Parents - 1 College Parent2 College Parents - 1 College Parent 0.00050.0005 0.00030.0003
2 College Parents - 0 College Parents2 College Parents - 0 College Parents1 College Parent - 1 College Parent1 College Parent - 1 College Parent
0.00000.00000.00030.0003
0.00000.00000.00020.0002
1 College Parent - 0 College Parents1 College Parent - 0 College Parents -0.0001-0.0001 -0.0001-0.0001
R2= 0.0001
Calibration Calibration Environmental Environmental
ParameterParameter ValueValue
# met initially, c# met initially, cinitinit 6.156.15
# met same college, c# met same college, ccollcoll 4.604.60
Probability same year, pProbability same year, pYEARYEAR .02.02
Probability same dorm pProbability same dorm pDORMDORM 0.350.35
cycles of friends of friendscycles of friends of friends 88
Probability meeting friend Probability meeting friend of friend (pof friend (pfrofrfrofr)) 0.540.54
Taste ParameterTaste Parameter ValueValue
ConstantConstant -1.72-1.72
Both WhiteBoth White 0.070.07
Both BlackBoth Black 2.102.10
Both HispanicBoth Hispanic 0.400.40
Both AsianBoth Asian 0.850.85
HiSATHiSAT 0.100.10
Parents EduParents Edu 0.090.09
ConservativeConservative 0.120.12
0
BB
HH
AA
WW
skillP arE du
C onserv
Segmentation by race vs. Segmentation by race vs. absolute and relative minority populationabsolute and relative minority population
y = -7.6794x + 4.1134
R2 = 0.0333
0
1
2
3
4
5
6
7
8
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Fraction Asian
P A
sian
& A
sian
/ P
an
y tw
o y = -64.315x + 10.71
R2 = 0.2566
0
2
4
6
8
10
12
14
16
18
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Fraction black
P B
lack
& B
lack
/ P
an
y tw
o
y = 0.0009x + 3.6018
R2 = 0.0231
0
1
2
3
4
5
6
7
8
0 200 400 600 800 1000 1200
Number of Asians
P A
sian
& A
sian
/ P
an
y tw
o
y = 0.0232x + 4.777
R2 = 0.1455
0
2
4
6
8
10
12
14
16
18
0 50 100 150 200 250 300
Number Black
P B
lack
& B
lack
/ /
P a
ny
two
Network FeaturesNetwork Features
0.0
05.0
1.0
15.0
2.0
25D
ensi
ty
0 50 100 150 200Number of friends