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. 2 Stages: Stage 1: Measure social network using a coordination game. Stage 2: Select players based on social distance to measure social preferences and trust.

3. 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

4. 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.

6. 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).

7. Network Elicitation Game: Tanya Alain Tanya names Alain

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

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

10. 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.

11. 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.

14. 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

15. 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)

16. Symmetric Friendships

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

18. 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)

22. How does social distance affect trust and social preferences? Use network data to design a non-anonymous experiment to study the role of social distance on trust.

23. What is Trust – some common definitions? “Firm reliance on the integrity, ability, or character of a person” (The American Heritage Dictionary) “Assured resting of the mind on the integrity, veracity, justice, friendship, or other sound principle, of another person; confidence; reliance;” (Webster’s Dictionary) “Confidence in or reliance on some quality or attribute of a person” (Oxford English Dictionary)

24. What is Trust? “Firm reliance on the integrity, ability, or character of a person” (The American Heritage Dictionary) “Assured resting of the mind on the integrity, veracity, justice, friendship, or other sound principle, of another person; confidence; reliance;” (Webster’s Dictionary) “Confidence in or reliance on some quality or attribute of a person” (Oxford English Dictionary) Define trust as my belief that another player is willing to sacrifice her utility to improve my utility.

25. Reasons to Trust: 1. TYPE TRUST: 2. EFFORT TRUST:

26. Reasons to Trust: The other player is altruistic and takes my utility into account. 1. TYPE TRUST:

27. Reasons to Trust: 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) 1. TYPE TRUST:

28. Reasons to Trust: 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) 1. TYPE TRUST: 2. EFFORT TRUST: The other player fears punishment in future interactions with me (or other players) if she does not take my utility into account.

29. Reasons to Trust: 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) 1. TYPE TRUST: 2. EFFORT TRUST: The other player fears punishment in future interactions with me (or other players) if she does not take my utility into account. Fear of punishment can differ by social distance (differently afraid of punishment from friends, friends of friends, friends of friends of friends or strangers)

30. Why not Trust (or Investment) Game? [Usually] studies one time anonymous encounters. Trusting behavior is not an equilibrium. Trust is often a result of repeated interactions. Moreover, not clear if trusting behavior is due to expectations of reciprocity or gambling (Karlan (2004))

31. Why not Trust (or Investment) Game? Usually studies one time anonymous encounters. In reality, trust is a result of repeated interactions. Trusting behavior is not an equilibrium. Moreover, not clear if trusting behavior is due to expectations of reciprocity or gambling (Karlan (2004)) Our solution: use real world social networks where trusting behavior is a result of agents playing a larger supergame.

32. 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

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).

34. 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 type and effort trust by varying the degree to which the recipient finds out about allocator’s actions.

35. 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 type and effort trust by varying the degree to which the recipient finds out about allocator’s actions. 3) Measure Recipients’ expectations about actions of allocators to understand to what extent type and effort trust exist and how accurately it is alligned with the decisions of allocators.

36. 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)

37. Reasons to Trust: The other player is altruistic and takes my utility into account. Anonymous Allocator/Anonymous Recipient (AA), Anonymous Allocator/Known Recipient (AK) 1. TYPE TRUST: 2. EFFORT TRUST: The other player fears punishment in future interactions with me (or other players) if she does not take my utility into account. Known Allocator/Anonymous Recipient (KA), Known Allocator/Known Recipient (KK)

38. Allocator Direct Friend Direct Friend Direct Friend Direct Friend 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. Indirect Friend 2 links Indirect Friend 3 links Share staircase Same house Who is the Recipient when known? (AK and KK)

39. 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.

40. Recipient Direct Friend Direct Friend Direct Friend Direct Friend 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 Indirect Friend 2 links Indirect Friend 3 links Share staircase Same house Recipients’ Expectations

41. Recipient Direct Friend Direct Friend Direct Friend Direct Friend 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 Indirect Friend 2 links Indirect Friend 3 links Share staircase Same house Recipients’ Expectations A possible pair

42. 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.

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

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

59. Allocator Direct Friend Direct Friend Direct Friend Direct Friend 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. Indirect Friend 2 links Indirect Friend 3 links Share staircase Same house Variable DISTANCE (Stranger) Dist = 0

60. Allocator Direct Friend Direct Friend Direct Friend Direct Friend 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. Indirect Friend 2 links Indirect Friend 3 links Share staircase Same house Variable DISTANCE (Stranger) Dist = 0 Dist = 1

61. Allocator Direct Friend Direct Friend Direct Friend Direct Friend Indirect Friend 2 links Indirect Friend 3 links Share staircase Same house Variable DISTANCE (Stranger) Dist = 0 Dist = 1 Dist = 2 Dist = 3

62. Allocator Direct Friend Direct Friend Direct Friend Direct Friend Indirect Friend 2 links Indirect Friend 3 links Share staircase Same house Variable DISTANCE (Stranger) Dist = 0 Dist = 1 Dist = 2 Dist = 3 Not significant in all specifications

63. 1) Take the set of 10 friends named by player 1 and intersect it with the set of 10 people named by player 2. Variable STRENGTH

64. 1) Take the set of 10 friends named by player 1 and intersect it with the set of 10 people named by player 2. 2) The intersection varies between 0 and 10. Divide this number by 10. This is the index of network strength. Variable STRENGTH

65. 1) Take the set of 10 friends named by player 1 and intersect it with the set of 10 people named by player 2. 2) The intersection varies between 0 and 10. Divide this number by 10. This is the index of network strength. A strong link exists between two people who have lots of common friends. Variable STRENGTH

66. 1) Take the set of 10 friends named by player 1 and intersect it with the set of 10 people named by player 2. 2) The intersection varies between 0 and 10. Divide this number by 10. This is the index of network strength. A strong link exists between two people who have lots of common friends. Variable STRENGTH A weak link exists between two people who have few common friends.

67. 1) Take the set of 10 friends named by player 1 and intersect it with the set of 10 people named by player 2. 2) The intersection varies between 0 and 10. Divide this number by 10. This is the index of network strength. A strong link exists between two people who have lots of common friends. Variable STRENGTH A weak link exists between two people who have few common friends. If STRENGTH is 0 then the two subjects have no friends in common at all.

68. 1) Take the set of 10 friends named by player 1 and intersect it with the set of 10 people named by player 2. 2) The intersection varies between 0 and 10. Divide this number by 10. This is the index of network strength. A strong link exists between two people who have lots of common friends. Variable STRENGTH A weak link exists between two people who have few common friends. If STRENGTH is 0 then the two subjects have no friends in common at all. Note that this measure is defined even if i and j are not friends and did not name each other. Generally, however, we would expect that STRENGTH decreases with social distance.

70. 3 situations Player 1 KNOWS player 2's identity and player 2 WILL FIND OUT the name of player 1 (effort trust) Player 1 KNOWS player 2's identity and player 2 WILL NOT FIND OUT the name of player 1 (type trust) Subjects divide 50 tokens that are worth: T=1: 1 token to the allocator and 3 to the recipient T=2: 2 tokens to the allocator and 2 to the recipient T=3: 3 tokens to the allocator and 1 to the recipient

71. Number of Tokens Held T=1T=2T=3 Recipient finds out (effort trust + type trust) 293540 Recipient does not find out (type trust) 344043

73. Regression

74. Player 2 Finds out (Effort Trust+Type Trust) Number of tokens held when recipient is not a friend.

75. Always give more to friends Player 2 Finds out (Effort Trust+Type Trust)

76. Always give more to friends Give more to friends of friends except in T3. Player 2 Finds out (Effort Trust+Type Trust)

77. Player 2 Does Not Find Out (Type Trust)

78. Number of tokens held when recipient is not a friend. Player 2 Does Not Find Out (Type Trust)

79. Number of tokens held when recipient is not a friend. Give more to direct friends only! Player 2 Does Not Find Out (Type Trust)

80. STRENGTH is statistically significant in T1 and T3. Player 2 Finds out (Effort Trust) Player 2 Finds out (Effort Trust+Type Trust)

81. STRENGTH wipes out the effect of DIST2 Player 2 Finds out (Effort Trust) Player 2 Finds out (Effort Trust+Type Trust)

82. DIST 1 and STRENGTH seem to have independent effects. Player 2 Finds out (Effort Trust) Player 2 Finds out (Effort Trust+Type Trust)

83. STRENGTH is statistically significant in T2. Player 2 Does Not Find Out (Type Trust)

84. DIST 1 and STRENGTH seem to have independent effects. Player 2 Does Not Find Out (Type Trust)

85. STRENGTH wipes out the effect of DIST3 in T2 Player 2 Does Not Find Out (Type Trust)

86. Unified Regression (fixed effects) Only Direct Friends Matter

87. Unified Regression (fixed effects) Strength only matters in non- anonymous case

88. Summary of Results - Allocators Give more to direct friends (compared to friends of friends, friends of friends of friends and unknown recipients) For non-anonymous interaction about 20 percent more tokens are passed to direct friends and about 8 percent more to indirect friends. For anonymous interaction about 15 percent more tokens are passed to direct friends. STRONG links (where two people have lots of friends in common) imply more giving across all three decisions in the NON-ANONYMOUS condition. This effect is large and about as big as the direct neighbor effect. Women seem to be less generous than men. Social distance effects are very similar EXCEPT for decision 3 where social network does not matter for men but it does matter for women.

89. Expectations about Player 1 Player 2 Finds out (Effort Trust+Type Trust) Expected Number of tokens held (Higher than actual!)

90. Expectations about Player 1 Player 2 Finds out (Effort Trust) Expected Number of tokens held (Higher than actual!) Expect direct and indirect links matter more so than they do! Expectations about Player 1 Player 2 Finds out (Effort Trust+Type Trust)

91. Expectations about Player 1 Player 2 Does not Find out (Type Trust) Expected Number of tokens held (Higher than actual!) Higher than non- anonymous! Expect direct and indirect links matter more so than they do!

92. STRENGTH doesn’t seem to have an independent effect! Expectations about Player 1 - Player 2 Finds out (Effort Trust+Type Trust)

93. STRENGTH is very important and wipes out DIST2 effect Expectations about Player 1: Player 2 Doesn’t Find out (Type Trust)

94. Summary of Results - Recipients RECIPIENTS - Confirm by and large the results for allocators. However: - subjects think that baseline giving is LOWER but that social distance matters MORE (by about a factor of 2) than it actually does - there is little difference between anonymous/non-anoymous treatment now - that means that subjects do not seem to properly factor in punishment - puzzling that STRONG links result is reversed: Network strength does matter in the anonymous case rather than the non-anonymous one. Theory would predict that strength matters more in the non-anonymous case because punishment mechanisms should work better if subjects have more common friends. - people are not as good in predicting giving between two different people

95. Summary of Results - Recipients Women believe allocators to be less generous than men Social distance effects are very similar EXCEPT for decision 3 where social network does not matter for men but it does matter for women (same for allocators).

96. Summary We find strong evidence for directed altruism. Need to add data on general altruism. We find also evidence for punishment and that punishment amplifies directed altruism. Interestingly - we find that STRONG links (where two people have lots of friends in common) imply more giving across all three decisions in the NON- ANONYMOUS condition. This effect is large and about as big as the direct neighbor effect.

97. Alternative Estimation Use CES utility is the value of my token, is the value of the other person’s tokens in decision d (d=1,2,3) m is the number of tokens held Constant elasticity of substitution:

98. Alternative Estimation: CES predicts Each player i chooses tokens held with error: Estimate and using NLLS (3 data points for each ) Run fixed effects regression as before:

99. Effort Trust: Gender Effects

100. Type Trust: Gender Effects

101. Gender Effects: Expectations about Player 1; Player 2 Finds out (Effort Trust)

102. Gender Effects: Expectations about Player 1; Player 2 Doesn’t Find out (Type Trust)