Measuring Social Capital in Real-World Social Networks

1. Measuring Social Capital in Real-World Social Networks Markus Mobius (Harvard University and NBER) Do Quoc-Anh (Harvard University) Tanya Rosenblat (Wesleyan University and CBRSS) October 2004

2. Social Capital (Putnam’s Definition) • Social capital refers to the collective value of all “social networks” [who people know] and the inclinations that arise from these networks to do things for each other [“norms of reciprocity”]

3. Social Capital • “Inclinations to do things for each other” can arise because of • innate altruistic preferences • cooperative behavior in a repeated game • The goal is to measure both sources depend on network structure

4. 2 Stages: • Stage 1: Measure social network using a coordination game. • Stage 2: Select players based on social distance to measure how social preferences vary with network structure.

5. Social Network • Residential social network of (569) upper-class undergraduates (sophomores, juniors and seniors) at a large private university. • Students are randomly allocated to 12 residential houses after their freshman year (as a blocking group of 2-8 students). • Students make long-term friendships within the houses (since houses provide meals, entertainment and educational activities). • 2 Houses used for the study

6. Methodology • Need high participation rate in order to get meaningful network data. • In addition to participation fee and experimental earnings, conduct a raffle with valuable prizes at the end of the study. • A major publicity campaign that advertises experiment (letters in the mail, posters, flyers, information table in the dining halls). • Direct emailing was not allowed until subjects signed up and agreed to receive emails.

8. Methodology • Networks are usually measured through surveys • Instead, use a coordination game with monetary payoffs to induce subjects think more carefully about their answers • Subjects name up to 10 friends and some dimensions of their friendship (e.g., how much time they spend together during the week).

9. Network Elicitation Game: Tanya names Alain Tanya Alain

10. Network Elicitation Game: Tanya gets a prize of $1 if Tanya Alain Tanya Alain Alain names Tanya

11. Network Elicitation Game: Tanya gets a prize of $1 if Tanya Alain Alain and Tanya get an additional prize if they agree on how much time they spend together each week. Tanya Alain Alain names Tanya; Alain also gets a prize of $1

12. Network Elicitation Game: Tanya Alain If T names A and A names T (coordinate) we call it a link; the link is stronger if there is agreement on the attributes of the relationship.

13. Network Elicitation Game: Tanya Alain In order to protect students’ feelings, each match is paid with 50% probability – so if they get 0, they don’t know whether this is because they were ‘rejected’, or because they were unlucky.

16. Network Data • In addition to the network game • Know who the roommates are • Geographical network (where rooms are located in the house) • Data from the Registrar’s office • Survey on lifestyle (clubs, sports) and socio-economic status

17. Network Data – Sample Description • House1 - 46% (259); House2 - 54% (310) • Sophomores - 31%(174); Juniors - 30% (168); Seniors - 40% (227) • Female - 51% (290); Male - 49% (279) • 5690 one-way relationships in the dataset; 4042 excluding people from other houses • 2086 symmetric relationships (1043 coordinated friendships)

18. Symmetric Friendships

19. Symmetric Friendships The agreement rate on time spent together (+/- 1 hour) is 80%

20. Network description • Cluster coefficient (probability that a friend of my friend is my friend) is .5841 • The average path length is 6.5706 • 1 giant cluster and 34 singletons • If ignore friends with less than 1 hr per week, many disjoint clusters (175)

24. How does social distance affect social capital? • Use network data to design a non-anonymous experiment to study the role of social distance on social capital.

25. Social Capital (Putnam’s Definition) • Social capital refers to the collective value of all “social networks” [who people know] and the inclinations that arise from these networks to do things for each other [“norms of reciprocity”]

26. Sources of Social Capital: 2. Cooperative Social Capital: 1. Preference-Based Social Capital:

27. Sources of Social Capital: 1. TYPE TRUST: 1. Preference-Based Social Capital: The other player is altruistic and takes my utility into account.

28. Sources of Social Capital: 1. TYPE TRUST: 1. Preference-Based Social Capital: The other player is altruistic and takes my utility into account. Altruism can differ by social distance (feel differently towards friends, friends of friends, friends of friends of friends or strangers)

29. Sources of Social Capital: 2. Cooperative Social Capital: 1. TYPE TRUST: 1. Preference-Based Social Capital: The other player is altruistic and takes my utility into account. The other player fears punishment in future interactions with me (or other players) if she does not take my utility into account. Altruism can differ by social distance (feel differently towards friends, friends of friends, friends of friends of friends or strangers)

30. Sources of Social Capital: 2. Cooperative Social Capital: 1. Preference-Based Social Capital: The other player is altruistic and takes my utility into account. The other player fears punishment in future interactions with me (or other players) if she does not take my utility into account. Altruism can differ by social distance (feel differently towards friends, friends of friends, friends of friends of friends or strangers) Fear of punishment can differ by social distance (differently afraid of punishment from friends, friends of friends, friends of friends of friends or strangers)

31. Experimental Design • Use Andreoni-Miller (Econometrica, 2002) GARP framework to measure altruistic types • A modified dictator game in which the allocator divides tokens between herself and the recipient. Tokens can have different values to the allocator and the recipient. • Subjects divide 50 tokens which are worth: • 1 token to the allocator and 3 to the recipient • 2 tokens to the allocator and 2 to the recipient • 3 tokens to the allocator and 1 to the recipient

32. Goals of the Experimental Design: 1) Measure Agent’s Altruistic Type and how their altruism varies with social distance (when allocators know the identity of the recipient).

33. Goals of the Experimental Design: 1) Measure Agent’s Altruistic Type and how their altruism varies with social distance (when allocators know the identity of the recipient). 2) Distinguish between preference-based and cooperative social capital by varying the degree to which the recipient finds out about allocator’s actions.

34. Goals of the Experimental Design: 3) Measure Recipients’ expectations about actions of allocators to understand to what extent recipients know about the services of social capital and how accurately it is alligned with the decisions of allocators (use this to study trusting behavior) 1) Measure Agent’s Altruistic Type and how their altruism varies with social distance (when allocators know the identity of the recipient). 2) Distinguish between preference-based and cooperative social capital by varying the degree to which the recipient finds out about allocator’s actions (use this to study “trustworthiness”)

35. Experimental Design • Each allocator participates in 4 treatments in random order: • Baseline: anonymous allocator and anonymous recipient (AA). • Anonymous allocator and known recipient (AK) • Known allocator and anonymous recipient (KA) • Known allocator and known recipient (KK) • With some uncertainty (always 15% chance that allocations are made by computer)

36. Sources of Social Capital: 2. Cooperative Social Capital: 1. Preference-Based Social Capital: The other player is altruistic and takes my utility into account. The other player fears punishment in future interactions with me (or other players) if she does not take my utility into account. Anonymous Allocator/Anonymous Recipient (AA), Anonymous Allocator/Known Recipient (AK) Known Allocator/Anonymous Recipient (KA), Known Allocator/Known Recipient (KK)

37. Who is the Recipient when known? (AK and KK) For Allocator choose 5 Recipients (in random order): 1 direct friend; 1 indirect friend of social distance 2; 1 indirect friend of social distance 3; 1 person from the same staircase; 1 person from the same house. Share staircase Indirect Friend 2 links Indirect Friend 3 links Same house

38. Experimental Design – What Do Recipients Do? • Recipients make predictions about how much they will get from an allocator in a given situation and how much an allocator will give to another recipient that they know in a given situation. • One decision is payoff-relevant: • => The closer the estimate is to the actual number of tokens passed the higher are the earnings. Incentive Compatible Mechanism to make good predictions Get $15 if predict exactly the number of tokens that player 1 passed to player 2 For each mispredicted token $0.30 subtracted from $15. For example, if predict that player 1 passes 10 tokens and he actually passes 15 tokens then receive $15-5 x $0.30=$13.50.

39. Recipients’ Expectations Recipients are asked to make predictions in 7 situations (in random order): 1 direct friend; 1 indirect friend of social distance 2; 1 indirect friend of social distance 3; 1 person from the same staircase; 1 person from the same house; 2 pairs chosen among direct and indirect friends Share staircase Indirect Friend 2 links Indirect Friend 3 links Same house

40. Recipients’ Expectations Recipients are asked to make predictions in 7 situations (in random order): 1 direct friend; 1 indirect friend of social distance 2; 1 indirect friend of social distance 3; 1 person from the same staircase; 1 person from the same house; 2 pairs chosen among direct and indirect friends A possible pair Share staircase Indirect Friend 2 links Indirect Friend 3 links Same house

41. Experimental Design • Within-subject design with randomized order of presentation: either all choices with “will find out” on one screen followed by “will not find out” screen; or “will find out/will not find out” on one screen for each choice.

42. Timing - Allocators: AA and AK or AA and AA Session 1; 1 decision from 1 pair chosen for monetary payoff (max $15)

43. Timing - Allocators: AA and AK or AA and AA KK and KA or KA and KK OR Session 2 (1 week later); 1 decision from 1 pair chosen for monetary payoff (max $15) Session 1; 1 decision from 1 pair chosen for monetary payoff (max $15)