measuring social capital in real-world social networks

Measuring Social Capital in Real-World

Social NetworksMarkus Mobius (Harvard University and NBER)Do Quoc-Anh (Harvard University)Tanya Rosenblat (Wesleyan University and CBRSS)

October 2004

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”]

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

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.

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

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.

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).

Network Elicitation Game:

Tanya Alain

Tanya names Alain

Network Elicitation Game:

Tanya Alain

Tanya Alain

Alain names Tanya

Tanya gets a prize of $1 if

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.

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.

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.

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

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)

Symmetric Friendships

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

140

Symmetric Friendships

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

140

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

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)

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.

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”]

Sources of Social Capital:1. Preference-Based Social Capital:1. Preference-Based Social Capital:

2. Cooperative Social Capital:2. Cooperative Social Capital:

Sources of Social Capital:

The other player is altruistic and takes my utility into account.

1. TYPE TRUST:1. TYPE TRUST:1. Preference-Based Social Capital:1. Preference-Based Social Capital:

Sources of 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)

1. TYPE TRUST:1. TYPE TRUST:1. Preference-Based Social Capital:1. Preference-Based Social Capital:

Sources of 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)

1. TYPE TRUST:1. TYPE TRUST:

The other player fears punishment in future interactions with me (or other players) if she does not take my utility into account.

1. Preference-Based Social Capital:1. Preference-Based Social Capital:

2. Cooperative Social Capital:2. Cooperative Social Capital:

Sources of 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)

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)

2. Cooperative Social Capital:2. Cooperative Social Capital:

1. Preference-Based Social Capital:1. Preference-Based Social Capital:

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 recipient2 tokens to the allocator and 2 to the recipient3 tokens to the allocator and 1 to the recipient

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).

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.

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).

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)

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”)

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)

Sources of Social Capital:

The other player is altruistic and takes my utility into account.

Anonymous Allocator/Anonymous Recipient (AA), Anonymous Allocator/Known Recipient (AK)

2. Cooperative Social Capital:2. Cooperative Social Capital:

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)

1. Preference-Based Social Capital:1. Preference-Based Social Capital:

DirectFriend

DirectFriend

Direct Friend

DirectFriend

Allocator

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.

IndirectFriend2 links

IndirectFriend3 links

Sharestaircase

Samehouse

Who is the Recipient when known? (AK and KK)

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.

DirectFriend

DirectFriend

Direct Friend

DirectFriend

Recipient

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

IndirectFriend2 links

IndirectFriend3 links

Sharestaircase

Samehouse

Recipients’ Expectations

DirectFriend

DirectFriend

Direct Friend

DirectFriend

Recipient

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

IndirectFriend2 links

IndirectFriend3 links

Sharestaircase

Samehouse

Recipients’ Expectations

A possible pair

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.

Timing - Allocators:

AA and AK

or

AA and AA

Session 1; 1 decision from 1 pair chosen for monetary payoff (max $15)

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)

DirectFriend

DirectFriend

Direct Friend

DirectFriend

Allocator

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.

IndirectFriend2 links

IndirectFriend3 links

Sharestaircase

Samehouse

Variable DISTANCE

(Stranger) Dist = 0

DirectFriend

DirectFriend

Direct Friend

DirectFriend

Allocator

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.

IndirectFriend2 links

IndirectFriend3 links

Sharestaircase

Samehouse

Variable DISTANCE

(Stranger) Dist = 0

Dist = 1

DirectFriend

DirectFriend

Direct Friend

DirectFriend

AllocatorIndirectFriend2 links

IndirectFriend3 links

Sharestaircase

Samehouse

Variable DISTANCE

(Stranger) Dist = 0

Dist = 1 Dist = 2 Dist = 3

DirectFriend

DirectFriend

Direct Friend

DirectFriend

AllocatorIndirectFriend2 links

IndirectFriend3 links

Sharestaircase

Samehouse

Variable DISTANCE

(Stranger) Dist = 0

Dist = 1 Dist = 2 Dist = 3

Not significant in all specifications

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

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

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

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.

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.

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.

3 situations

Player 1 KNOWS player 2's identity and player 2 WILL FIND OUT the name of player 1 (cooperative + preference-based social capital)

Player 1 KNOWS player 2's identity and player 2 WILL NOT FIND OUT the name of player 1 (preference-based social capital)

Subjects divide 50 tokens that are worth:T=1: 1 token to the allocator and 3 to the recipientT=2: 2 tokens to the allocator and 2 to the recipientT=3: 3 tokens to the allocator and 1 to the recipient

Number of Tokens Held

T=1 T=2 T=3

Recipient finds out (preference-based and cooperative)

29 35 40

Recipient does not find out (preference-based) 34 40 43

Regression

Player 2 Finds out (Preference Based + Cooperative)

Number of tokens held when recipient is not a

friend.

Always give more to friends

Player 2 Finds out (Preference Based + Cooperative)

Always give more to friends

Give more to friends of friends

except in T3.

Player 2 Finds out (Preference Based + Cooperative)

Player 2 Does Not Find Out (Preference-Based)

Number of tokens held when recipient is not a

friend.

Player 2 Does Not Find Out (Preference-Based)

Number of tokens held when recipient is not a

friend.

Give more to direct friends only!

Player 2 Does Not Find Out (Preference-Based)

STRENGTH is statistically

significant in T1 and T3.

Player 2 Finds out (Preference Based + Cooperative)

STRENGTH wipes out the

effect of DIST2

Player 2 Finds out (Preference Based + Cooperative)

DIST 1 and STRENGTH seem to have independent

effects.

Player 2 Finds out (Preference Based + Cooperative)

STRENGTH is statistically

significant in T2.

Player 2 Does Not Find Out (Preference-Based)

DIST 1 and STRENGTH seem to have independent

effects.

Player 2 Does Not Find Out (Type Trust) Player 2 Does Not Find Out (Preference-Based)

STRENGTH wipes out the

effect of DIST3 in T2

Player 2 Does Not Find Out (Type Trust) Player 2 Does Not Find Out (Preference-Based)

Unified Regression (fixed effects)

Only Direct Friends Matter

Unified Regression (fixed effects)

Strength only matters in

non-anonymous

case

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.

Application to Trust:

One of the services of social capital is trust Results on preference-based and

cooperative social capital measure “trustworthiness” of players.

Can ask a question about “trusting” behavior by measuring expectations of recipients about the behavior of allocators.

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)

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.Define trust as my belief that another player is willing to sacrifice her utility to improve my utility.

Expectations about Player 1Player 2 Finds out (Effort Trust+Type Trust)

Expected Number of tokens held

(Higher than actual!)

Expectations about Player 1Player 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 1Player 2 Finds out (Effort Trust+Type Trust)

Expectations about Player 1Player 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!

STRENGTH doesn’t seem to

have an independent

effect!

Expectations about Player 1 - Player 2 Finds out (Effort Trust+Type Trust)

STRENGTH is very important and wipes out DIST2 effect

Expectations about Player 1: Player 2 Doesn’t Find out (Type Trust)

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

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).

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.

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:

iiiijddijijddijijd mqsmpsU

1

]))50()1(()[(

ii

1

1

dp dq

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:

ijdijiijdijd smy ),(

),( ijiijd sm

i ijsijs

ijiijijijij DISTDISTDISTs 321 321

Effort Trust: Gender Effects

Type Trust: Gender Effects

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

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