The Old Boy (and Girl) Network: Social Network Formation on University Campuses

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The Old Boy (and Girl) Network Social Network
Formation on University Campuses

• Adi Mayer and Steve Puller
• Texas AM

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Motivation to Study Social Networks in Higher
Education

• Social networks determine peer effects in
  college
• Sacerdote (2001), Zimmerman (2003), Winston and
  Zimmerman (2003), Kremer and Levy (2003),
  Stinebrickner Stinebrickner (2005),
• Does race affect social interaction / are
  universities really integrated?
• Sacerdote Marmaros (2006)
• Information transmission
• Granovetters Strength of Weak Ties

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Motivation Role of Social Networks in Labor
Market

• Social Connections are important for job search
• While the frequency of alternative job-finding
  methods varies somewhat by sex and occupation,
  the following generalization seems fair
  approximately 50 of all workers currently
  employed found their jobs through friends and
  relatives (Montgomery 1991)
• Determination of Wages / Employment
• Job search through social networks generates
• positively correlated employment across agents
  and time
• positive duration dependence of unemployment
• social networks can generate inequality between
  two otherwise equivalent groups
• Calvo-Armengol and Jackson (2004), Pellizarri
  (2004), Ioannides and Soetevent (2006), Arrow and
  Borzekowski (2004)

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Empirical Approach In This Paper

• 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

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What determines the formation of social networks?
Do individuals have contact?
Environment
Preferences / Tastes
Do individuals want to be friends?
Social network
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What determines the formation of social networks?
Preferences / Taste
Environment
Social network

• Race
• Parental background
• Political orientation
• Abilities

• Composition of student body
• Curriculum
• Dorm assignment
• Clubs / Activities

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What determines the formation of social networks?
Preferences / Taste
Environment
Social network

• Race
• Parental background
• Political orientation
• Abilities

• Composition of student body
• Curriculum
• Dorm assignment
• Clubs / Activities

Policy Instruments
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Model of Network formation

• Simulate Network
• Stage 1 Students meet with probability varying
  in institutional features (e.g. same dorm)
• Stage 2 Conditional upon meeting, students form
  friendships based upon tastes for observable
  characteristics
• Stage 3 Students meet friends of friends with
  some probability, and again may form friendships
• Calibrate parameters of model so simulated
  network resembles actual network
• Perform Counterfactual Experiments
• Turn off institutional effects and make all
  meeting random
• Turn off tastes and make all liking random
• X-Percent Rule add more students with specific
  characteristics

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Preview of Results

• University social networks exhibit standard
  features of social networks
• E.g. Clustering
• Networks exhibit only modest segmentation in some
  dimensions (ability, parental education,
  political orientation), but substantial
  segmentation by race
• University policies have very limited ability to
  reduce segmentation by race

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Data

• From facebook.com
• 10 universities in Texas
• Texas AM registrar
• Additional administrative data

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www.facebook.com

• Online student social network directory for each
  university
• Need official University e-mail to sign up
• Started on February 4, 2004 at Harvard
• By July 2006, 7th most visited website in US

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Data

• From facebook.com
• All student profiles as of 1/17/05 for 10
  universities in Texas
• 65,104 undergraduates
• (Self-reported) Demographics year, birthdate,
  gender, high school, hometown, major, current
  courses, dating status, residence hall, political
  orientation, jobs, hobbies
• Social network links to friends at own-school
  other schools
• Race we classify based upon pictures
• Texas AM registrar
• Race, College performance (GPA), High school
  performance (SAT, class rank), Parental
  characteristics (income, parents education),
  College activities

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The 10 Universities
University Undergrad Enrollment Facebook sample Fraction in Facebook
Rice 2,933 2,354 0.80
U Texas 36,473 14,728 0.40
Texas AM 35,605 15,797 0.44
Baylor 11,521 7,008 0.61
Texas Tech 23,329 7,219 0.31
Texas Christian 7,024 3,678 0.52
SMU 6,090 3,496 0.57
U North Texas 24,274 4,474 0.18
UT Arlington 18,176 1,442 0.08
Texas State 22,402 4,908 0.22
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Texas AM Students In Facebook Overall Student Population
GPR 2.95 2.93
SAT 1168 1152
High School ile Class Rank 86.5 86.0
Texas Resident 97.4 97.4
Female 55.2 50.6
In a Greek 14.3 11.6
Lives in a dorm 41.1 33.7
Athlete 2.5 2.5
Freshman 27 22
Sophomore 27 22
Junior 26 26
Senior 20 29
White 81.8 80.5
Hispanic 11.4 12.0
Asian 4.0 3.8
Black 2.3 2.9
Father College Degree 61 58
Mother College Degree 54 51
Household Income lt 40,000 14 17
Household Income gt 80,000 53 48
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Segmentation by Race (Table 5) Relative
probability of friendship
 Pair of   Rice Baylor Texas AM U Texas
White/Hisp White/H White/Hisp White/H 1.03 1.10 1.01 1.12
White/Hisp Asian White/Hisp Asian 0.79 0.43 0.74 0.42
White/Hisp Black White/Hisp Black 0.87 0.41 0.77 0.56
Asian Asian Asian Asian 2.41 4.24 7.42 4.13
Asian Black Asian Black 0.92 0.52 1.01 0.54
Black Black Black Black 5.12 5.99 16.54 13.13
Any two students Any two students 1 1 1 1
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Segmentation by Race (Table 5) Absolute
Segmentation
  Rice Baylor Texas AM U Texas
Fraction of Students White/Hisp 0.82 0.91 0.96 0.85
Fraction Friends of Whites/Hisp who are White/Hisp 0.85 0.96 0.97 0.93

Fraction of Students Asian 0.13 0.03 0.02 0.13
Fraction Friends of Asians who are Asian 0.30 0.25 0.16 0.58

Fraction of Students Black 0.05 0.06 0.02 0.02
Fraction Friends of Blacks who are Black 0.25 0.47 0.27 0.38
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Segmentation by Political Orientation (Table 6)
    Rice Baylor Texas AM U Texas
Fraction of Students Liberal Fraction of Students Liberal 0.32 0.08 0.06 0.23
Fraction Friends of Lib. who are Lib. Fraction Friends of Lib. who are Lib. 0.38 0.12 0.10 0.29
Fraction of Students Conservative Fraction of Students Conservative 0.15 0.47 0.54 0.23
Fraction Friends of Cons. who are Cons. Fraction Friends of Cons. who are Cons. 0.21 0.58 0.63 0.39

Pair of Relative probability of friendship Relative probability of friendship Relative probability of friendship Relative probability of friendship
Liberal Liberal Liberal Liberal 1.22 1.13 1.28 1.06
Liberal Conservative Liberal Conservative 0.86 0.59 0.69 0.75
Conservative Conservative Conservative Conservative 1.35 1.41 1.28 2.17
Any two students Any two students 1 1 1 1
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Segmentation by Major (Table 6)
  Rice Baylor Texas AM U Texas
Fraction of Students in Same Major if Friends Random 0.04 0.02 0.02 0.02
Fraction of Students in Same Major 0.08 0.06 0.07 0.08
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Structure of Networks (Table 3)
  Rice Baylor Texas AM U Texas
Avg. Number of Friends 50.8 59.8 41.1 39.5
Variance of Friends 31.9 50.8 38.4 36.5
Skewness of Friends 1.06 1.74 2.06 2.01
Cluster Coefficient 0.24 0.19 0.17 0.20
Cluster Coefficient Conservatives 0.28 0.21 0.18 0.24
Cluster Coefficient Liberals 0.24 0.16 0.14 0.19
Cluster Coefficient Blacks 0.44 0.30 0.32 0.37
Cluster Coefficient Asians 0.31 0.30 0.26 0.25
Avg. Degrees of Separation 2.30 2.62 2.95 3.00
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Rest of Paper Texas AM only
Sample All pairs of students in facebook that
are matched to TAMU records and we observe all
characteristics.
Linear probability model

• 7,719 students
• N(N-1)/2 29,787,621 pairs
• 0.34 of all pairs are friends

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Linear probability model

• Regress Friends Y/N on
• Race (e.g. White-White, White-Black, etc.)
• High School, Cohort, Gender
• Family Background
• Dorm, Academic
• Ability
• Activities

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Predictors of friendship (Table 8)
R2
Race 0.0006
High School, Age, Gender 0.0293
Family Background 0.0001
Dorm, Academic 0.0033
Ability 0.0001
Activities 0.0032
All Covariates 0.0360
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Predictors of friendship Dorm /Academics
Only Dorm, Academic All Covariates
Coef Coef
Constant 0.0028 0.0028
Same Dorm 0.0426 0.0407
Same Major 0.0038 0.0030
Same College 0.0018 0.0016
R2 0.0033
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Predictors of friendship Activities
Only activities All Covariates
Coef Coef
Constant 0.0030 0.0028
Both are Athletes 0.0649 0.0635
Both in Corps of Cadets 0.0536 0.0428
Both are Greek 0.0192 0.0188
One is Greek -0.0003 -0.0003
One is Athlete -0.0003 -0.0003
One in Corps of Cadets -0.0005 -0.0004
R2 0.0032
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Predictors of friendship Race
Baseline Probability of friendship 0.34 percent
Only Race All Covariates
Coefficient Coefficient
Constant 0.0026 0.0028
Both Black 0.0562 0.0542
Both Asian 0.0132 0.0126
Both Hispanic 0.0028 0.0027
Hispanic - Black 0.0011 0.0010
Both White 0.0011 0.0009
Asian - Black 0.0008 0.0010
Hispanic - Asian 0.0002 0.0005
White - Hispanic 0.0001 0.0003
White - Black -0.0001 -0.0002
White - Asian -0.0002 -0.0002
R2 0.0006
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Effect of common friends? (Table 9)
of common friends -- 0.0298
Constant 0.0028 -0.0003
Both Black 0.0542 0.0151
Both Asian 0.0126 0.0071
Both Hispanic 0.0027 0.0013
Same High School 0.1859 0.1379
Same Year in College 0.0010 0.0012
Same Gender 0.0000 -0.0005
Same Dorm 0.0407 0.0214
Same Major 0.0030 0.0024
Both are Athletes 0.0635 0.0111
Both are Greek 0.0188 -0.0083
R2 0.0360 0.2456
Note all covariates included but not reported
? Endogenous effects through friends of friends
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Friends of friends matter

• Magnification of exogenous network determinates
• Simple prediction based on reduced from
  estimation misleading
• Model network formation

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A model of network formation

• Understand process and determinants . of
  network formation
• Meeting vs. Taste
• Friends of friends
• Generate counterfactuals
• Policy evaluation

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A model of network formation

• Random Graph Theory
• - cannot explain network features like
  clusteredness
• Jackson Rogers (2005)
• Random Meeting Search
• - Generates network features
• - No preferences
• - No institutions / environmental differences
• We add
• (1) environmental differences
• (2) preferences that determine friendship
  conditional on meeting

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A model of network formation

• Observe features of real network
• Simulate network model for set of parameters
• Calculate features of simulated network
• Pick parameters so that features of simulated and
  actual network are as similar as possible

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Graph Theoretic Description of Network

• n students
• g is n x n friendship matrix
• iff i,j are friends
• otherwise

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Network formation

• Initially g0
• 1) Meet random students
• Like each other?
• Yes gt gij1
• 2) Meet students in same environment
• Like each other?
• Yes gt gij1
• 3) Meet friends of friends
• Like each other?
• Yes gt gij1

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Network formation

• Random Meeting
• Each student meets each other student with
  probability pinit
• Meet students from same environment
• Meet other students in same college with
  probability picoll
• Each student in same cohort with probability
  pYEAR
• Each other student in same dorm with probability
  pDORM
• Meet friends of friends
• Each student i meets all friends of their friends
  (gik1 and gkj1)
• with probability pfrofr
• Repeated S times

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Network formation

• Friendship formation conditional on meeting
• Two students who met become friends if
• g(i,j) I(Uij(.) ci) I (Uji (.) cj)
• I ( f (Xi,Xj,uijß ) gt 0)
• where Uij utility to i of being friends with j
• ci marginal cost of friendship to student i
• X observable characteristics
• u unobservable characteristics

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Network formation
Two students i,j who met become friends if
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Key Assumptions

• Unobserved tastes are uncorrelated with
  institutional meeting channels
• e.g. No taste for other engineering majors
• Unobserved determinants of meeting are
  uncorrelated with observable taste
  characteristics
• e.g. No Black/Hispanic Student Association
• Assessing validity from reduced-form regressions
• Coefficients of College/Cohort/Dorm are robust to
  inclusion of covariates on Race/Family
  Background/Ability
• Coefficients of Race/Family Background/Ability
  are robust to inclusion of College/Cohort/Dorm

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Model Fit
Moments Entering Calibration Sample of 1930 Students Full 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
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Counterfactual Experiments

• Simulate counterfactual network changing
• Institutions that affect meeting probability
• Preferences for friends with specific
  characteristics
• Friend of friends meeting channel

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Counterfactual Experiments

• Simulate counterfactual network changing
• Institutions that affect meeting probability
• Preferences for friends with specific
  characteristics
• Friend of friends meeting channel

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Counterfactual Experiments

• Simulate counterfactual network changing
• Institutions that affect meeting probability
• Preferences for friends with specific
  characteristics
• Friend of friends meeting channel

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Counterfactual Experiments

• Simulate counterfactual network changing
• Institutions that affect meeting probability
• Preferences for friends with specific
  characteristics
• Friend of friends meeting channel

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Counterfactuals Meeting
Moments Entering Calibration Full 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
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Counterfactuals Preferences
Moments Entering Calibration Full 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
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Counterfactuals Double Hispanic Students
Moments Entering Calibration Full 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
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Counterfactuals Introduction to Minorities
Policy introduce each white to 1 of minorities
and each minority to 1 of whites
Moments Entering Calibration Full 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
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Counterfactuals

• Environment has little influence on segmentation
  by race, ability, background
• Affirmative action increases absolute segregation
  of minority, but exposes more white students to
  minority students
• Introduction - small effect on absolute
  segregation, increases exposure of whites to
  minority students.

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Conclusion

• Social networks at universities are segmented
• Social networks at universities exhibit classic
  characteristics
• Limited potential for policies that make
  encounters more random

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Other Future Research Possibilities

• Measure peer effects on educational outcomes
• Grades (data for TAMU)
• First jobs (TAMU students report at graduation)
• Peer effects in high school
• Analyze effects of school splits along
  socioeconomic lines on social integration
• Effect of random college/dorm assignment at Rice
• Field experiment measure transmission of
  information through network by disseminating job
  ads

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THE END
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Network Features

• Clusteredness
• Are the friends of your friends also your friends?

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Predictors of friendship High-school / Age
Only High School, Age All Covariates
Coef. Coef.
Constant 0.0039 0.0028
Same High School 0.1864 0.1859
Same Gender 0.0006 0.0000
Same Year in College 0.0010 0.0010
Difference b/t Yrs in College -0.0013 -0.0011
R2 0.0293
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Predictors of friendship Background
Only Family Background All Covariates All Covariates
Coef Coef
Constant 0.0027 0.0028 0.0028
Both from High Income Households 0.0006 0.0002 0.0002
Both from Low Income Households 0.0002 0.0002 0.0002
2 College Parents - 2 College Parents 0.0014 0.0009 0.0009
2 College Parents - 1 College Parent 0.0005 0.0003 0.0003
2 College Parents - 0 College Parents 1 College Parent - 1 College Parent 0.0000 0.0003 0.0000 0.0002 0.0000 0.0002
1 College Parent - 0 College Parents -0.0001 -0.0001 -0.0001
R2 0.0001
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Calibration
 Environmental Parameter  Value
met initially, cinit 6.15
met same college, ccoll 4.60
Probability same year, pYEAR .02
Probability same dorm pDORM 0.35
cycles of friends of friends 8
Probability meeting friend of friend (pfrofr) 0.54

 Taste Parameter  Value
Constant -1.72
Both White 0.07
Both Black 2.10
Both Hispanic 0.40
Both Asian 0.85
HiSAT 0.10
Parents Edu 0.09
Conservative 0.12
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Segmentation by race vs. absolute and relative
minority population
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Network Features