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

1. The Old Boy (and Girl) Network: Social Network Formation on University Campuses Adi Mayer and Steve Puller Texas A&M

2. 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 • Granovetter’s “Strength of Weak Ties”

3. 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)

4. 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

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

6. 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

7. 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

8. Policy Instruments Preferences 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

9. 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

10. Data • From facebook.com • 10 universities in Texas • Texas A&M registrar • Additional administrative data

11. 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

14. 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 A&M registrar: • Race, College performance (GPA), High school performance (SAT, class rank), Parental characteristics (income, parents’ education), College activities

15. The 10 Universities

18. Segmentation by Race (Table 5)Relative probability of friendship

19. Segmentation by Race (Table 5)“Absolute” Segmentation

20. Segmentation by Political Orientation (Table 6)

21. Segmentation by Major (Table 6)

22. Structure of Networks (Table 3)

23. Rest of Paper: Texas A&M 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

24. 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

25. Predictors of friendship (Table 8)

26. Predictors of friendship:Dorm /Academics R2= 0.0033

27. Predictors of friendship: Activities R2= 0.0032

28. Predictors of friendship: Race Baseline Probability of friendship = 0.34 percent R2= 0.0006

29. Effect of common friends? (Table 9) Note: all covariates included but not reported  Endogenous effects through friends of friends

30. Friends of friends matter • Magnification of exogenous network determinates • Simple prediction based on reduced from estimation misleading Model network formation

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

32. 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

33. 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

34. Graph Theoretic Description of Network • n students • gis nx nfriendship matrix • iff i,j are friends • otherwise

35. 1) Random 2) Environment 3) Fr of Fr Network formation • Initially g=0 • 1) Meet random students • Like each other? Yes => gij=1 • 2) Meet students in same environment • Like each other? Yes => gij=1 • 3) Meet friends of friends • Like each other? Yes => gij=1

36. Network formation • Random Meeting Each student meets each other student with probabilitypinit • 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 (gik=1 and gkj=1) with probability pfrofr • Repeated S times

37. 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,uij;β ) > 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

38. Network formation Two students i,j who met become friends if:

39. 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

40. Model Fit

41. Random Instit. Fr of Fr Counterfactual Experiments • Simulate counterfactual network changing… • Institutions that affect meeting probability • Preferences for friends with specific characteristics • Friend of friends meeting channel

42. Random Instit. Fr of Fr Counterfactual Experiments • Simulate counterfactual network changing… • Institutions that affect meeting probability • Preferences for friends with specific characteristics • Friend of friends meeting channel

43. Random Instit. Fr of Fr Counterfactual Experiments • Simulate counterfactual network changing… • Institutions that affect meeting probability • Preferences for friends with specific characteristics • Friend of friends meeting channel

44. Random Instit. Fr of Fr Counterfactual Experiments • Simulate counterfactual network changing… • Institutions that affect meeting probability • Preferences for friends with specific characteristics • Friend of friends meeting channel

45. Random Instit. Random Instit. Random Instit. Fr of Fr Fr of Fr Fr of Fr Random Instit. Fr of Fr Counterfactuals: Meeting

46. Random Instit. Fr of Fr Random Instit. Fr of Fr Random Instit. Fr of Fr Counterfactuals: Preferences

47. Counterfactuals: Double Hispanic Students

48. Counterfactuals: Introduction to Minorities Policy = introduce each white to 1% of minorities and each minority to 1% of whites

49. 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.

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