Preliminary

An Experimental Test of Risk-Sharing Arrangements

Gary Charness University of California, Santa Barbara

Garance Genicot

Georgetown University

February 2004

ABSTRACT

We investigate risk sharing without commitment by designing an experiment to match a

simple model of voluntary insurance between two agents when aggregate income is constant. Participants are matched in pairs. Each period, they receive their income with or without the random component h; after observing own and counterpart income, each person in a pair can decide to make a transfer to the other person. It is common information that there is a given probability that all pairs will be dissolved at the end of each period, with participants re-matched. At the end of the experiment, one period is randomly drawn to count for cash payment. Participants all face the same variance in their income, but do not necessarily have the same mean income. This setting allows us to experimentally test different implications of risk sharing without commitment. In particular, we find strong evidence of risk sharing and reciprocal behavior, where transfers are higher with a higher continuation probability and with a higher degree of risk aversion. However, transfers are lower with inequality, in contrast with existing models of both risk sharing and social preferences. JEL Classification Numbers: A49, C91, C92, D31, D81, O17. Key Words: experiments, gift exchange, informal insurance, risk-sharing, social preferences. We are grateful to the California Social Science Experimental Laboratory at UCLA, particularly to Patricia Wong for arranging the logistics and to Raj Advani for expert programming. We also thank seminar participants at the NEUDC at Yale University, the World Bank DECRG, Princeton University and Boston University for their helpful suggestions; all errors are of course our own. We thank the UCSB Academic Senate for partially funding for our experiments. Please, address all correspondence to gg58@georgetown.edu and charness@ucsb.edu.

1. INTRODUCTION

Risk is a pervasive fact of life for most people, especially in developing countries.

Individuals have often been shown to respond to the large fluctuations in their income by engaging

in informal risk-sharing by providing each other with help in the form of loans, gifts and transfers

in time of need. There is considerable empirical evidence that risk-sharing provides some but

limited insurance in village communities (Deaton, 1992, Townsend, 1994, Udry, 1994, Jalan and

Ravallion, 1999, Ligon, Thomas and Worrall, 2002, Grimard, 1997, Gertler and Gruber, 1997,

Foster and Rosenzweig, 2002).

The most important limitation appears to arise from the lack of enforceability of these risk-

sharing agreements. The fact that these agreements must be designed to elicit voluntary

participation often seriously limits the extent of insurance they can provide. A growing theoretical

literature provides a characterization of the optimal self-enforcing risk-sharing agreement and

some of its consequences (Kimball (1988), Coate and Ravallion (1993), Kocherlakota (1996),

Kletzer and Wright (2000), Ligon, Thomas and Worrall (2002), Genicot and Ray (2003) and

Genicot (2003)).

In this project, we experimentally test different implications of these models of risk-sharing

without commitment. We chose a very simple model with two agents in which, each period, one

of the two agents, selected at random, receives an amount of money h (in addition to his or her

fixed income). The model is described in detail in the next section. We then designed an

experiment that closely matches the model. Participants are matched in pairs. Each period, they

receive their income with or without the random component h, and after observing their own and

counterpart's incomes, each person in a pair can decide to make a transfer to the other person. It is

common knowledge that there is a given probability that all pairs will be dissolved at the end of

each period, with participants re-matched. At the end of the experiment, one period is randomly

drawn to count for cash payment. Participants all face the same variance in their income, but do

not necessarily have the same mean income.

Of course, positive experimental transfers do not by themselves prove that risk sharing is

taking place, since a transfer could instead reflect some form of altruism or social preference. If

transfers do in fact represent reciprocal risk-sharing behavior, we would expect to see certain

patterns in the data. For example, we would expect that a longer time horizon should lead to a

higher level of risk sharing, while recent models of (distributional) social preferences would

predict no difference in behavior as we vary the expected length of the interaction between two

parties. We would also expect to see a correlation between a person’s degree of risk aversion and

the attractiveness of a risk-sharing relationship; on this point, social-preference models are (strictly

speaking) agnostic. Finally, do past transfers by the other individual in a match affect the transfers

one makes? Again, this would be expected with reciprocal exchange, but not if transfers are

driven by social preferences that reflect only distributive concerns.

We find evidence in support of risk sharing in the laboratory. Average transfers double

when there is a 90% likelihood that a match will continue into the next round compared to when

there is an 80% likelihood of continuation. We measure risk-aversion using a simple investment

choice and find a significant positive relationship between one’s degree of risk aversion and one’s

transfer choices. Moreover, reciprocal behavior is shown to be an important factor: the higher the

first transfer made by an individual’s partner within a match, the higher the individual’s transfer

made upon receiving a good shock.

Since we examine matches where the individuals have the same fixed income as well as

matches featuring unequal fixed payoffs, we test for the effect of ex ante inequality on risk sharing.

Genicot (2003) studies risk sharing between two agents facing the same income fluctuations and

same preferences but differing in their fixed income, and shows that inequality helps risk sharing

in a large range of cases. Since we keep the expected difference in post-shock payoffs the same in

both types of match, social-preference models with linear specifications1 (e.g., Fehr and Schmidt

1999; Charness and Rabin 2002) would predict no difference in transfers across conditions, if we

consider the one-round payoffs.2

We instead find that inequality actually decreases risk sharing. We discuss possible

explanations based on both ease of coordination and one’s identity (as in Akerlof and Kranton

2000) as an ex ante ‘poor’ or ‘rich’ person, consistent with results in social psychology such as

Tajfel, Billig, Bundy, and Flament (1970), who find that subjects strongly favor members of their

experimental ingroup, even in a situation devoid of the usual trappings of ingroup membership.

We also find that males do significantly more transfers than females, especially when the

female tendency towards greater risk aversion is taken into account.

Previous experimental work on risk-sharing is rather limited. Bone et al. (2000) report an

experiment designed to test whether pairs of individuals are able to exploit efficiency gains in the

sharing of a risky financial prospect (taking advantage of their difference in risk aversion, with

commitment). Their results indicate that fairness is not a significant consideration, but rather that

having to choose between prospects diverts partners from allocating the chosen prospect

efficiently. The pattern of agreements suggests that, where allocation is the sole issue, partners

largely favor ex ante efficiency over ex post equality. From the transcripts there is little indication

that ex post fairness is a significant consideration.

1 The Bolton and Ockenfels (2000) and Cox and Friedman (2002) models can accommodate non-linearity in payoff ratios or differences; their predictions in this case depend on parameter values. 2 However, if instead consider the basis for comparison to be each person’s expected payoff in the match, then these models would also predict more risk sharing with inequality.

The most closely related experiment to ours is perhaps Selten et al.’s (1998) Solidarity

Game since our risk-sharing experiment would degenerate into something close to a solidarity

game if the match continuation probability described in Section 3 was null. In their game, each of

three players has an ex ante independent 2/3 chance of winning 10 DM and a 1/3 chance of

receiving nothing. Before learning the outcome, each player decides on an amount that she

commits to give to one loser or to each of two losers, if she actually won the 10 DM and there are

one or two losers. They found that the great majority of subjects were willing to make some

conditional gifts. However the design of their experiment and the fact that transfers are asked from

winners only may be driving some of their results. They distinguish five behavioral types, with the

most common type (36%) giving the same positive total amount to one loser and to two losers.

This behavior does not lend itself to a straightforward interpretation as the result of altruistic utility

maximization.3

In a field experiment in Zimbabwe, Barr (2003) conducted some one-shot risk-sharing

games among villagers who have been observed to share risk with each other. Prior to choosing a

lottery in which they want to participate, individuals are explicitly provided with the some risk-

sharing option either with commitment to equal split, or, in other village, with possibility to keep

one’s return without this being directly told to others (though they can infer some information from

the payoff they receive, especially in small groups). She finds a larger participation in risk-sharing

groups, larger groups and more risk-taking in the first case. Looking at the possibility of publicly

revealing withdrawals from risk-sharing, she concludes that both intrinsic and extrinsic

motivations are important. However, the experiment being conducted, without anonymity, among

3 Subjects were also asked to estimate the average gifts of others. There is a significant positive correlation between the estimates and the subjects' own gifts. This is similar to the false-consensus effect known in the literature (e.g., Ross et al., 1977). Among male subjects, those studying economics show a more “egoistical” behavior than others. Among female subjects, no such “education effect” can be found. Females tend to give more than males.

people who know each other, and the lack of commitment in the choice of lottery makes the

interpretation of these results unclear.

Finally, also relevant might be Goeree, Holt and Palfrey [2000] that examines experimental

results for a variety of generalized matching penny games, and find that simple two-parameter

model that combines quantal response equilibrium and risk aversion explains the observed choice

patterns. They find that alternative explanations based on inequality aversion are not supported by

the data. Their risk aversion estimates, around .5, are significant and of approximately the same

magnitude as our estimates in this experiment as well as estimates recovered from several different

auction experiments and auction field data.

The remainder of our paper is organized as follows. The next Section lays out the basic

model of risk-sharing without commitment and describes some important implications. Section 3

then presents the experimental design. In Section 4, the main results of the experiment are

presented. Section 5 discusses the implications and some limitations of the paper, and Section 6

concludes.

2. A MODEL OF RISK-SHARING WITHOUT COMMITMENT

A standard model of risk sharing without commitment goes as follows. Time is discrete

and the number of period is infinite. In each period t, two agents, indexed by i ∈{1,2}, receive an

income yi and one of them, randomly chosen, incur a fixed monetary gain h. They each have a

probability ½ to receive h but the aggregate income is constant at Y = y + y + h in each period.

The following table summarizes the income distribution of the two agents:

State 1

(proba ½)

State 2

(proba ½)

Agent 1 y + h y

Agent 2 y y + h

In line with standard practice, let us assume that all agents have additively time-separable

Von Neumann-Morgenstern utility functions defined over consumption, such that the expected

lifetime utility at time t is given by

∑∞

=+

0)(

j

ijti

jt cuE δ for all i∈{1, 2}.

where ui’>, ui’’ <, limc→0 ui (c) = - ∞, and δ ∈ (0,1) is the discount rate. The operator Et is the

expectation conditional on what is known at time t.

Since individuals are risk-averse, optimality would require that the ratio of their marginal

utilities remains constant over time and across states of nature. When the aggregate income is

constant, this implies keeping each individual’s consumption at a constant level. The exact levels

depend on the welfare weights used but must sum to the aggregate income and satisfy the

voluntary participation constraint. If c* is the optimal level of consumption for individual 1, then

it must be that

++≥−

++≥

∗

∗

)(21)(

21)(

)(21)(

21)(

22222

11111

yuhyucYu

yuhyucu

As motivated and discussed in the Introduction, we focus on the theme that insurance

arrangements must be self-enforcing, and that this requirement constrains the form of such

arrangements. The enforcement constraint refers to the possibility that at some date, an individual

who is called upon to make transfers to others in the community refuses to make those transfers.

To be self-enforcing, a risk-sharing agreement must be such that the expected net benefits from

participating in the agreement is at any point in time larger than the one time gain from defection.

The literature on risk-sharing concentrates on the constrained optimal or ‘second-best’ self-

enforcing schemes. It follows that the constraint is modeled by supposing that a deviating

individual is excluded from the insurance pool, so that he must bear stochastic fluctuations on his

own (or given an equivalent continuation utility). That is, a risk-sharing agreement resulting in a

stream of consumptions titc ∀}{ for individual i must be such that, at any period t,

∑∑∞

=+

∞

=+ +≥+

11)()()()(

j

ijti

jt

iti

j

ijti

jt

iti zuEzucuEcu δδ for all i∈{1, 2} (1)

where itz is the total income of individual i at time t (the sum of iy and h if received the good

shock this period).

If the power of such punishment is limited, then perfect insurance may not be possible.

However, even when full risk-sharing is not possible, individuals may be able to design a risk-

sharing agreement by limiting transfers in states for which the enforcement constraint is binding

(see Coate and Ravallion (1993) and Kocherlakota (1996) among others).

It is well known that with this simple distribution, when a first best is not incentive

compatible, the constrained optimal agreement is characterized by two values, t*, the transfer

made by 1 to 2 when 1 received h and, t*, the transfer made by 2 to 1 when 2 received h. These

transfers are such that the incentive constraints (1) hold with equality for both agents, that is t* =

(t*, t*,) is defined by

)(2

)()2

1()(2

)()2

1(

)(2

)()2

1()(2

)()2

1(

2222122222

1111211111

yuhyutyuthyu

yuhyutyuthyu

δδδδ

δδδδ

++−=++−+−

++−=++−+−

∗∗

∗∗

(2)

A smaller transfer can be asked to one of the agents as long as only she has received h in order to

give to this agent a larger share of the surplus. However, as soon as the state in which the other

agent receives h occurs then the constrained optimal agreement is stationary and consists of t*.

A first implication of this model is that, when full insurance is not achieved, a higher

discount rate δ increases the weight put on the long term gain from insurance relative to the short

term gain from deviating. There are threshold values δ and δ , with 10 <<< δδ , such that for

values of δ smaller or equal to δ no risk-sharing is possible, for ),( δδδ ∈ there is come but

constrained insurance, and for values of δ greater or equal to δ first best risk-sharing can be

achieved. When constrained, a higher δ raises the transfers that individuals are able to make to

each other and so the insurance that they can provide for each other.

A second implication of this model is that an overall increase in the risk aversion exhibited

by the agents increases t* and the level of risk-sharing that individuals can achieve, by increasing

the long term gain from insurance. For instance, if individuals have utility indicator

i

ii

ρ

ρ−

−= 1c

11(c)u , where ρi is the Arrow-Pratt coefficient of relative risk aversion, then it is easy

to show that an increase ρi relaxes i’s incentive constraint (2), thereby improving insurance.

Finally, what is the effect of inequality? Let’s consider different values of y and

y keeping the aggregate income Y constant. Clearly, if y = y both individuals are ex-ante

identical. Now, increasing y and decreasing y to keep Y unchanged would make 1 relatively

richer than 2 while keeping the variance of their income constant. To be sure, the set of Pareto

optimal allocations is unaffected since the aggregate income is the same. However, the division of

wealth affects the autarchic utility and thereby does affect the set of self-enforcing allocations.

Genicot (2003) shows that for a large range of utility functions such spread-preserving inequality

between the two agents increases the likelihood of first-best risk-sharing and increases the transfer

that agents make to each other within the constrained optimal agreement.

In what follows, we describe an experiment in which we replicated the setting of this model

of risk-sharing without commitment and test specific features of risk sharing, such as the various

effects of risk aversion, beliefs, inequality, and the expected time horizon on the transfers chosen.

3. EXPERIMENTAL DESIGN

All the experiments reported here were conducted at the CASSEL Laboratory in UCLA.

We had six sessions, with an even number of participants ranging from 12 to 18 in a session

(depending on show-ups). Participants earned an average of about $17, including a $5 show-up

fee, for about an hour of their time. The procedures that we followed are described below and the

complete experimental instructions for the δ = .9 treatment are shown in the Appendix. Note that

participants were never told the nature of the experiment; in particular the terms risk-sharing or

insurance were never used during the experiment.

Prior to the main experiment, we first asked people to complete an investment question.

Each person was provisionally endowed with 100 experimental units and could invest any portion

of this amount in a risky asset that had a 50% chance of success and paid 2.5 times the amount

invested if successful. The decision-maker retained the units not invested. We told the

participants that we would later choose two people at random in each session for actual payoff

implementation, and a coin was flipped after the session to determine success or failure for these

investors. The objective of this investment question was two-fold. First, it provides us with a

measure of risk aversion for each individual.4 To be sure, the higher the investment the less risk

averse the individual is. Second, we use the answer to this question in the main experiment to

match individuals with similar degrees of risk aversion.

The body of the session then consisted of a number of matches. The features of this

experiment were designed to closely fit the model presented in Section 2. For the duration of each

match, every participant was paired with one other person. To reduce heterogeneity, we paired

people who had invested more (less) than 67 in the risky investment with other people who had

invested more (less) than 67. Each match was comprised of an uncertain number of periods or

rounds that was determined as follows: After each round, the computer determined (for all current

matches) whether another round would follow. In three of our sessions (Treatment 1), the

continuation probability was 80%, and in the other three sessions (Treatment 2), the continuation

probability was 90%. In the first case, the expected number of subsequent rounds in a match (at

any point in time after the first round) was four; in the latter case, the expected number of

subsequent periods was nine; the participants in the corresponding sessions were informed of this

mathematical fact.

The continuation probability is designed to play the same role in the decision process of the

experimental subjects as the discount factor in Section 2. This also avoids the unraveling problem

resulting when the number of rounds in any match is known in advance. Ex ante, we therefore

expected each match to last five rounds in Treatment 1 and ten rounds in Treatment 2. When the

4 Naturally inducing risk aversion on the participants rather than relying on their preferences would allow us to have a more accurate measure of risk aversion. Unfortunately, there is little evidence that the method used to induce risk aversion, the binary lottery procedure, works and a couple of studies actually showing that it does not work (Camerer and Ho 1994, Selten et al. 1999). The lack of reliable methods for inducing risk neutrality or controlling for risk attitudes and social preferences in experiments complicates direct empirical testing of theories based on richer behavioral assumptions.

matches ended, all participants were randomly re-matched for the next match. We had ten matches

in each 80% session and seven matches in each 90% session.

In each round, each person will received income, which was comprised of a fixed portion

and an amount that was added to the fixed income for that round for one of the people in each

match. The person receiving this extra amount was randomly chosen in each pair for every round

of the match. The fixed portions did not vary during the match, but did change from match to

match. In some matches, both fixed portions were 70 units, while in other matches one fixed

portion was 20 and the other was 120. In all cases, the amount randomly assigned and added was

200 units. This income distribution corresponds to the two-state distribution with constant

aggregate income described in Section 2.

In the beginning of each round, each participant learned his or her fixed income, the fixed

income of the other person in the match, and which one of them received the extra 200 in that

round. Everyone then chose a non-negative amount, not to exceed the income received, to transfer

to the other person and these designated amounts were then transferred. We allowed individuals to

make transfers whether or not they had received the 200 units as we did not want to bias the

experiment in favor of risk-sharing, and as we did not want the subjects to infer the main topic of

the experiment. Participants saw a history of the income and transfers for each previous round in

that match, and could also review their previous matches.

Finally, we needed to avoid possible wealth effects in payoffs. If every round was

contributing to their payoffs, individuals would care about the distribution of the sum of income

net of transfers over all rounds instead of the income net of transfers earned in each round. To

solve this and make sure that the subjects face similar decisions than in the model described in

Section 2, we chose only one round (of the many that were played in the session) for conversion of

experimental payoff units to real dollars, at the rate of 17 experimental units to $1. All of this was

indicated in the instructions.

We also asked participants for some information about their decisions and expectations in

the beginning of the first and fourth matches. Specifically, the individuals who received h were

asked: “what motivates your choice of transfer?” and the others (who did not receive h) were

asked: “what transfer do you expect the other person to give you?” At the end of the session,

participants answered questions concerning their gender and major before receiving their payoff.

4. MAIN RESULTS

We first present some summary statistics about our data and then discuss in turn several

important questions in relation to our results:

Question 1: Does a higher continuation probability increase the amount of risk-sharing?

Question 2: Does a higher degree of risk aversion increase insurance?

Question 3: What is the effect of inequality on risk-sharing (matches with equal fixed portions

versus matches with unequal fixed portions)?

Question 4: How does time and past transfers affect risk sharing?

Question 5: Do demographics such as gender and major affect the transfer chosen?

Question 6: How do transfers react to unmet expectations?

Table 1 shows the average transfer made in each session, and the overall average for each

treatment:

Table 1: Average Transfer, by Session and Treatment

Avg. Transfer # Observations Std. Dev.

Session 1 15.83 656 27.91

Session 2 14.97 416 21.19

Session 3 13.42 384 27.12

Treatment 1 (δ=.8) 14.95 1456 25.95

Session 4 38.84 1162 48.31

Session 5 28.46 648 37.38

Session 6 20.96 846 34.94

Treatment 2 (δ=.9) 30.61 2656 42.54

A first observation is that a substantial amount of transfer takes place. With a continuation

probability of 80% (Treatment 1), we see an average transfer of about 15 and, with a continuation

probability of 90% (Treatment 2), the average transfer is around 30. The overall transfer is more

than twice as high when the continuation probability is 90% instead of 80%. The Wilcoxon-

Mann-Whitney ranksum test (see Siegel and Castellan, 1988) on session-level data, a most

conservative test that considers each session as only one observation, finds that transfers are

significantly higher in Treatment 2 (p = 0.050, one-tailed test).5

This aggregation ignores the substantial heterogeneity present in the population, indicated

by the large standard deviation. Figure 1 shows the frequency with which each range of transfer is

made in the two treatments:

5 Throughout the paper, we round p-values to three decimal places.

0%

10%

20%

30%

40%

50%

Prop

ortio

n in

Ran

ge

0-10 10-20 20-30 30-40 40+Avg. Individual Transfer

Figure 1 - Distribution of Avg. Individual Transfers

Treatment 1Treatment 2

We see a great diversity of average individual transfers, particularly in Treatment 2. The

Wilcoxon test on individual average transfers (not completely independent) confirms that these are

higher in Treatment 2 (Z = 3.54, p = .000).

While overall individual transfers are an important metric, it is not clear what to make of

positive transfers when a participant has received less income in the round than the other matched

person. These may have some value through signaling one’s cooperative nature, or may simply

represent confusion. A better metric may be average transfers made when the chooser has the

higher income. Table 2 shows these by session and treatment:

Table 2: Average Transfer when got h, by Session and Treatment

Avg. Transfer # Observations Std. Dev.

Session 1 26,54 328 34.61

Session 2 22.28 208 26.14

Session 3 20.43 192 34.37

Treatment 1 (δ=.8) 23.71 728 32.42

Session 4 64.08 581 54.54

Session 5 43.31 324 43.59

Session 6 34.20 423 43.76

Treatment 2 (δ=.9) 49.49 1328 50.48

Figure 2 gives the distribution of individual average transfers made when ahead:

0%

10%

20%

30%

40%

50%

Prop

ortio

n in

Ran

ge

0-15 15-30 30-45 45-60 60+Avg. Individual Transfer

Figure 2 - Dist. of Average Transfers Given when h

Treatment 1: delta=0.8Treatment 2: delta=0.9

The average transfer made when ahead is higher in every session in Treatment 2, when the

continuation probability is 0.9, than it is in Treatment 1, with a continuation probability of 0.8, and

this average transfer when ahead is always higher than the corresponding overall average transfer

in each session. Figure 2 shows a pattern similar to that seen in Figure 1, but with higher levels of

average individual transfers. In fact, the average transfer when ahead was higher than the average

transfer when behind for 85 individuals, and this was reversed for eight people.6 A simple

binomial test (See Siegel and Castellan, 1988) finds this to be extremely significant (Z = 7.98, p =

0.000). It is clear that people are not just randomly and arbitrarily transferring money, but are

instead quite sensitive to which matched person receives higher income in the round. 6 The remaining person always chose a transfer of 0.

It is also useful to consider the average transfer made in each match. The distribution of

these average transfers is shown in Figure 3:

0%

10%

20%

30%

40%

50%

Prop

ortio

n in

Ran

ge

0-10 10-20 20-30 30-40 40+Avg. Individual Transfer

Figure 3 - Distribution of Avg. Transfers, by Match

Treatment 1: delta=0.8 Treatment 2: delta=0.9

The difference between treatments in Figure 3 is perhaps even stronger than in Figures 1 and 2. A

Wilcoxon test confirms the difference is highly significant (Z = 5.96, p = 0.000).

Another way to see that individuals in a match are insuring each other is to consider the

standard deviation of realized consumption for a pair of individuals in a match.7 In the absence of

transfers, they would face a standard deviation of about 100. Table 3 illustrates clearly that, by

making transfers to each other, individuals are sharing risk. This is particularly true under

Treatment 2 (high continuation probability) and when the fixed income of the individuals is equal

(y1 = y2 =70) as opposed to unequal (yi =20, y-i =120 for i =1,2 ).

Table 3: Average Std. Dev. of Consumption

Avg. Std. Dev. of Consumption

# Matches

7 Note that in this simple model the standard deviation of consumption of individuals matched with each other will be the same.

Treatment 1 Equal 85.07 110

(δ=0.8) Unequal 90.65 110

Treatment 2 Equal 75.39 100

(δ=0.9) Unequal 84.18 45

Thus far we have established that we see significant transfers and that these transfers are

highly dependent on whether the chooser has received h or not. Hence, individuals are sharing

risk. Moreover, the transfers and risk-sharing are definitely higher when the continuation

probability increases, and when individuals have the same fixed-income.

In the aggregate, the average transfer from the h person was 34.03 with inequality and was

47.50 with equality. Table 4 provides a breakdown, by continuation probability and fixed income,

of average transfers after receiving h:

Table 4: Average Transfer when receiving h, by fixed income and treatment

Fixed Income

20 70 120

Treatment 1 (δ = 0.8) 16.31 28.19 25.80

Treatment 2 (δ = 0.9) 32.07 55.95 54.61

We see that average transfers are lowest for people with a fixed income of 20, and are actually a

bit higher with a fixed income of 70 than with a fixed income of 120.

To address the questions listed at the beginning of this section and study the determinants

of the transfers that individuals make, we supplement our non-parametric statistical analysis with

some regression analysis. To account for unobserved individual characteristics, we use individual

effects. Table 5 presents the results of the pooled, fixed effect, and random-effect regressions on

all the transfers made and Table 6 presents the regressions for only the transfers made when the

individual has received h.

[Table 5 and 6 here]

In both cases, the F-test strongly rejects the hypothesis that all individual constants are the

same in the fixed-effect model. A Hausman test does not reject the random effect hypothesis that

the individual effects are uncorrelated with the other regressors. Hence, the discussion will be

based on the random effect estimation.

Before we examine the effects listed in the beginning of the section, note that Table 5

shows that receiving h clearly increases the transfers. The coefficient on Varinc (equal to 200 if

the individual received h and 0 otherwise) implies that receiving h increases the average transfer

by 23 units when the fixed income (yi) is 20, by 36.6 when the fixed income is 70 and by 28.2

when the fixed income is 120.

Question 1: continuation probability. In both Table 5 and 6, we see that a higher

continuation probability substantially increases the transfers (coefficients on Delta), and this effect

increases over time within a match (coefficient on Round*Delta). According to random-effects

specification (column 6) in Table 5, increasing the continuation probability from .8 to .9 increases

the transfers by 9.5 units in the first round and by an additional 1.6 units in each subsequent round.

We see a similar pattern in Table 6, with transfers about 14 units higher initially and an additional

2.6 higher in each subsequent round, given a greater likelihood of continuation.

Question 2: risk aversion. Our initial investment question provides us with an estimate of

individual attitude towards risk. 8 As illustrated in Figure 4, we observed a large range of answers

to this investment question.

In both Table 5 and 6, the coefficients on Invest (the amount invested in the risky

investment) are significantly negative in all specifications. A larger investment in the risky asset

meaning less risk aversion, a negative impact on the transfers is exactly what we would expect.

We conclude that a higher degree of risk aversion increases the transfer that one chooses when

high and so risk sharing. The random effect specification (columns (5) and (6)) of Table 6 shows

that an h-receiving individual who chose to invest 30 in the risky asset would transfer 13 or 14

units more than a similar individual who chose to invest 80 in the risky asset. The partner’s

investment in the risky asset has also a negative impact on the transfers but become insignificant

once we control for the first transfer made by the partner within a match.

Question 3: inequality. Looking at the effect of the fixed income on transfers, we can

assess the overall effect of equality. Remember changes to an individual’s fixed income are

concurrent with changes in his partner’s income. Table 5 shows that these two forces result in a

strong non-linear effect of yi, first increasing then decreasing. The estimated coefficients on the

dummy variables for a fixed income of 70 (D70) and for a fixed income of 120 (D120) show a

linear effect of the fixed income on the transfers, while the interactions of these dummies with

Varinc show that the transfers when ahead are increased by 13.8 units when both individuals have

an income of 70 (see coefficients on D70*Varinc and D120*Varinc). The overall effect on the

8 Assuming constant relative risk aversion, the risk aversion would be given by

ρ ≡ln(1.5)

ln(inv *2.5 +100 - inv) - ln(100 - inv)

0

if inv <100if inv =100

.. An investment choice of 25 therefore corresponds to ρ = .67,

an investment choice of 50 corresponds to ρ = .32, and an investment choice of 75 corresponds to ρ = .19.

transfer when ahead is a large increase for a fixed income of 70 as opposed to 20, but then hardly

any change when comparing an income of 120 with an income of 70. As a result, the overall effect

of equality on the insurance within a match is significantly positive. This is exactly what we see in

Table 6, the transfers when receiving h are about 14 higher when the fixed income is 70 than when

the fixed income is 20, while the transfers when the fixed income is 120 are about 20 higher than

when the fixed income is 20.9

We can supplement our regression analysis here by considering whether each individual

made larger transfers on average with equality or inequality, since each person participated in both

environments. It turns out that average transfers were higher for 60 people with equality and for

32 people with inequality, with no difference for the other two people. The binomial test finds this

difference highly significant (Z = 2.92, p = 0.004, two-tailed test).

Question 4: past transfers and time. Risk-sharing requires reciprocity. We see that the

first transfer made by the individual’s partner within a match has a strong positive effect on his

transfers. In Table 5, we see that an additional unit of transfer in the first period by one’s

counterpart (Other’s 1st tr) increases an individual’s average transfer in each period by 16 cents,

and in Table 6, an additional unit of transfer in the first period by one’s counterpart increases an

individual’s average transfer when he receives h by 24 cents per period. This is irrespective of the

counterpart’s income realization at the time (the coefficient on Other’s 1st tr|h is not significant).

This suggests that individuals are coordinating in their levels of transfers and that transfers made

by an individual when he has not received h may have some signaling value.

We find very different evolution of transfers over time within matches, depending on

whether the individuals’ fixed incomes are the same or not. When the individuals have the same 9 There was not much difference in the transfers made by the person not receiving h with equality and inequality. These averaged 10.40 with equality and 9.20 with inequality.

fixed income, transfers within a match tend to increase over time. In contrast, in an unequal

situation the transfers are essentially flat or even slightly decreasing over time.

Question 5: demographic. The average transfer by males was 28.9 while the average

transfer by females was 22.0. This is surprising given that there is a difference in risk aversion

across gender, as is often observed, with female being more risk averse than male, so that we

might have expected females to make higher transfers. Using random effects and controlling for

other factors, we also observe in Table 5 and 6 a modest but significant gender effect, as females

make smaller transfers than males do. The lower transfers by females results in a significantly

lower net consumption for males (Z = 2.68, p = 0.007, using a Wilcoxon test on individual average

consumption.10 We also tested (not shown) for the role of students’ major on the transfers made,

and found virtually no effect.

Question 5: beliefs. In the first round of a couple of matches per session, we elicited the beliefs of

subject who did not receive the 200 regarding the transfer they expect to receive from the other.

We find that, out of 94 observations, 38% of them received more than they did expect, 9%

received exactly what they expected and 53% received less than expected. These percentages do

not vary by continuation probability or across gender, and the difference between matches with

equal and unequal fixed income are not significant.

Table 7: Average Transfer when got h, by Session and Treatment

Equality Dummy

Received: 0 1 Total

Less than 28 22 50

10 Note that this is not due to females having better draws; females comprised 56.4% of the population and females had the larger endowment 55.6% of the time.

Expected 29.79 % 23.40% 53.19%

3 5 8 As Expected 3.19% 5.32% 8.51%

16 20 36 More than Expected 17.02% 21.28% 38.30%

47 47 94 Total 50.00% 50.00% 100.00%

Table 8 shows the effect of meeting individual’s expectations or not on the transfers. Bdiff takes

values +1, 0, -1 if the transfer received earlier in the current match was above, at or below

expectations. Clearly, its effect is significant and positive on the transfers made by an individual.

It is interesting to see that the effect of the round within the match losses its significance now that

we control for the meeting of expectations.

5. DISCUSSION

Our experiment provides some strong support for the model of risk-sharing without

commitment. First, there is strong evidence that individuals are providing some but limited

insurance to each other. Net positive transfers are going from individuals receiving a high shock to

the other and these transfers substantially reduces the standard deviation of consumption. Second,

transfers are limited in a way that is consistent with the relatively low level of risk aversion

exhibited by the participants.11 A longer expected time horizon has a strong positive effect on

transfers, as does a higher degree of risk aversion. None of these effects would be expected to

arise if transfers are motivated purely by altruism or distributive preferences. As we also find that

one’s chosen transfer depends positively on the other party’s first transfer and on receiving

transfers that meet or exceed expectations, there are clear evidence of reciprocal relationship.

11 These levels of risk aversion are similar to the ones found in other experiments.

While all of these factors support the risk-sharing model presented in Section 2, the effect of

inequality on transfers is negative rather than positive. For utility functions of the HARA class

(hyperbolic absolute risk aversion), inequality should improve risk sharing and not decrease it;

with decreasing risk aversion (as traditionally assumed) we should observe that individuals with

lower fixed income making higher transfers when receiving h than individuals with higher fixed

income make when receiving h, as the poorest agent trades mean consumption in exchange for

insurance. Yet, in our experiment we observe that high-fixed-income individuals actually transfer

more than low-fixed-income individuals.

Of course, individual preferences may be very different from HARA utility functions. The

fact that the person with more fixed income makes higher transfers is consistent with social

preferences. However, the fact that overall transfers are lower with inequality also goes against the

consensus of the social-preference models.

In some sense equal fixed payoffs make coordinating on reciprocal transfers easier, but this

does not seem the only effect. Table 4 clearly shows that the inequality results are driven by the

fact that people make substantially lower transfers when they have a low fixed income. In a

certain sense, this seems reasonable, since even when the person with the low fixed income

receives h, he or she is nevertheless poorer in expected terms during the remainder of the match.

Since we pay for only one period, this story might not apply, but it still feels plausible. In any

event, by this logic we should also see substantially higher transfers with the high fixed income

than with equal fixed incomes, and we don’t.

In some sense equal fixed payoffs make it easier for one to identify with the other person

and interpret the transfers made. Previous studies have shown that participants in experiments are

prone to identification or ‘solidarity’ with an arbitrary group. Tajfel, Billig, Bundy, and Flament

(1970) find that subjects treat people who have been designated to be part of their ‘group’ quite

differently than people not in their group. Charness, Rigotti, and Rustichini (2003) achieve strong

group identification and coordination in Battle-of-the-Sexes games with partisan audiences. If, as

Akerlof and Kranton (2000, p. 748) assert, “a person’s self is associated with different social

categories and how people in these categories should behave,” perhaps it is reasonable to expect

that people with similar average income levels would more readily form reciprocal relationships

than people with very different average incomes. Ex ante equality may also set up an egalitarian

frame, leading to more sharing. More tests are clearly needed to better understand these results.

6. CONCLUSION

In this paper, we have attempted to test experimentally for risk-sharing without

commitment and some of its implications. The experiment was designed to fit as closely as

possible the models of risk-sharing without commitment used in the literature, and, following the

literature, we focused on the constrained optimal equilibrium.

We found significant support for some important features of the models of risk sharing

without commitment. It is striking that a higher continuation probability and a higher degree of

risk aversion significantly increase the level of risk sharing that individuals achieve. Moreover,

reciprocity is shown to be important for risk-sharing: the higher the first transfer made by an

individual’s partner within a match, the higher the individual’s transfer, especially upon receiving

a good shock. We also find that beliefs matter, in that how actual transfers compare to expected

transfers plays a role in subsequent transfers. Far from increasing risk sharing, inequality between

individuals in a match actually decreases it, suggesting the influence of some form of social

cohesion or identification process.

REFERENCES

Akerlof, G. and R. Kranton (2000), “Economics and Identity,” Quarterly Journal of Economics, 115, 715-753.

Barr, Abigail, “Risk Pooling, Commitment, and Information: An experimental test of two fundamental assumptions,” mimeo.

Bolton, G.E., and A. Ockenfels (2000), “ERC – A Theory of Equity, Reciprocity, and Competition”, American Economic Review 90, 166-193 Bone, J., J. Hey and J. Suckling (2003), “A Simple Risk-Sharing Experiment,” forthcoming Journal of Risk and Uncertainty. Camerer, C. and T. Ho (1994), “Isolation Effects and Violation of Compound Lottery Reductions,” mimeo. Charness, G. and M. Rabin (2002), “Understanding Social Preferences with Simple Tests,” Quarterly Journal of Economics, 117, 817-868. Charness, G., L. Rigotti, and A. Rustichini (2003), “They are Watching You: Audience Effects in Economic Institutions,” mimeo. Coate, S. and M. Ravallion (1993), “Reciprocity without Commitment: Characterization and Performance of Informal Insurance Arrangements,” Journal of Development Economics 40, 1--24. Deaton, A. (1992), Understanding Consumption. Oxford: Clarendon Press. Fehr, E. and K. Schmidt, 1999. A theory of fairness, competition, and cooperation. Quarterly Journal of Economics 114, 817-868.

Foster, A. and M. Rosenzweig, “Imperfect Commitment, Altruism, and the Family: Evidence from Transfer Behavior in Low-Income Rural Areas,” Review of Economics and Statistics 83, 389--407. Genicot, G. (2003), “Inequality and Informal Insurance,” mimeo.

Genicot, G. and D. Ray (2003) “Endogenous Group Formation in Risk-Sharing Arrangements,” Review of Economic Studies 70 (1), 2003.

Gertler, P. and J. Gruber (2002), “Insuring Consumption Against Illness,” American Economic Review 92, 51-70.

Goeree, J., C. Holt and T. Palfrey (2000), “Risk Averse Behavior in Generalized Matching Pennies Games,” Games and Economic Behavior, forthcoming Grimard, F. (1997), “Household Consumption Smoothing through Ethnic Ties: Evidence from Côte D'Ivoire,” Journal of Development Economics 53, 391--422. Jalan, J. and M. Ravallion (1999), “Are the Poor Less Well Insured? Evidence on Vulnerability to Income Risk in Rural China,” Journal of Development Economics 58, 61--81. Kimball, M. (1988), “Farmer Cooperatives as Behavior Toward Risk,” American Economic Review 78, 224--232. Kletzer, K. and B. Wright (2000), “Sovereign Debt as Intertemporal Barter,” American Economic Review 90, 621--639. Kocherlakota, N. (1996), “Implications of Efficient Risk Sharing without Commitment,” Review of Economic Studies 63(4), 595-609. Ligon, E., J. Thomas and T. Worrall (2002), “Mutual Insurance and Limited Commitment: Theory and Evidence in Village Economies,” Review of Economic Studies 69, 209-44. Selten, R., and A. Ockenfels (1998), “An Experimental Solidarity Game,” Journal of Economic Behavior and Organization 34, 517-519. Selten, R., A. Sadrieh, and K. Abbink (1999), “Money Does Not Induce Risk Neutral Behavior, But Binary Lotteries Do Even Worse,” Theory and Decision 46, 211-49. Townsend, R. (1994), “Risk and Insurance in Village India,” Econometrica 62(3), 539-91. Townsend, R. (1995), “Consumption Insurance: An Evaluation of Risk-Bearing Systems in Low-Income Economies,” Journal of Economic Perspectives 9(3), 83-102. Udry, C. (1994), “Risk and Insurance in a Rural Credit Market: An Empirical Investigation in Northern Nigeria,” Review of Economic Studies 61(3), 495-526. Udry, C. (1995), “Risk and Saving in Northern Nigeria,” American Economic Review 85(5), 1287 1300.

APPENDIX

Instructions

Welcome to our experiment. For showing up on time, we will pay you a $5 show-up fee. In addition, you may receive additional earnings as the result of the outcomes in the experimental session. Today’s session will take about an hour. To begin, we ask you to complete a brief questionnaire. The body of the session will be comprised of a number of segments. In each of these segments, each participant will be matched with one other person. Each segment is comprised of an uncertain number of periods. The number of periods in a segment is determined as follows: After each period, the computer will ‘roll a die’ (for the entire room) to see whether another period will follow, with a 90% chance that another period will follow, and a 10% chance that the segment ends immediately. The computer will ‘roll the die’ after every period. With this continuation probability, the expected number of subsequent periods in a segment, at any point in time, is 9. When the segment ends (10% chance after each period), all participants will be randomly re-matched with other participants for the next segment. We anticipate that there will be approximately 7 segments in the session, but this will vary according to how many periods there are in the segments – we aim to complete the session in about an hour. In each segment, you and the person with whom you are matched will receive income. This income is composed of a fixed portion and an amount (200) that is added to the fixed income for that period for one of the people in each match; the person receiving this extra amount is randomly chosen in each pair for every period of the segment. The fixed portions will not vary during the segment, but will change from segment to segment; these fixed portions may or not be the same for the two people matched. In all cases, this fixed portion will be considerably smaller than the 200 units that are randomly assigned. In the beginning of the period, you will learn your fixed income, the fixed income of the person with whom you are paired, and who received the extra 200 in the period. At this point, you choose to transfer money to the other person. This amount must be non-negative and no more than the total income you received in that period. The other person in your match simultaneously chooses to transfer money to you, subject to the same restrictions on the amount to be transferred. The designated amounts are then transferred, and the computer then determines whether another period follows in this segment. You will see a history of the income and transfers for each previous period in that segment. Thus, you will be involved in many periods. We wish to make it clear that only one of these periods will be chosen at random for conversion to real dollars, at the rate of 17 experimental units to one cash dollar.

Let’s take an example. Assume that your fixed income be 50 and that you are matched with someone whose fixed income is 90. In each round, either you get an additional 200 (50% chance) or the person with whom you are matched gets an additional 200 (50% chance). If in this round the other person receives this 200, your total income is 50 while his or her total income is 290. Now, you and the person with whom you are matched decide on transfers. Suppose you transfer x to the other person while he or she transfers y to you; then your “income net of transfer” or “consumption” for this round is 50-x+y while his “income net of transfer” or “consumption” for this round is 290-y+x. If this round happens to be the one selected to count for actual payoffs, these are your and your match’s payoffs for the experiment. For instance if x = 1 and y = 61 then your payoff would be 110 and your match’s payoff would be 230. At some points along the way, you will be asked for some information about your decisions and/or your expectations. The history of income and transfers for the current match appears on your screen. By pressing the “full view” button you can also review the history of your past matches. At the end of the experiment, one period will be chosen at random for payment. The screen will state your earnings. When you have completed a short questionnaire on your demographics, we will distribute receipts forms for participants to sign, and will pay people individually and privately. We highly encourage clarifying questions. Thank you for your participation.

0%

8%

16%

24%

32%

40%

% o

f pop

ulat

ion

20 orless

21-40 41-60 61-80 81-100

Investment

Figure 4 - Amounts Invested in the Risky Investment

Preliminary

Table 5 - Transfer Regressions (1) (2) (3) (4) (5) (6) Transfer

Given ols ols fe fe re re

Investment -0.093 -0.136 -0.127 -0.134 [0.024]** [0.030]** [0.063]* [0.065]*

Other’s Inv -0.070 -0.068 0.020 0.021 0.009 0.010 [0.025]** [0.025]** [0.028] [0.028] [0.027] [0.027]

Female dummy -9.055 -5.231 -6.914 -5.441 [1.060]** [1.368]** [2.991]* [3.078]

Female other 2.060 1.652 1.571 1.620 1.571 1.634 [1.052] [1.061] [1.122] [1.119] [1.104] [1.102]

Other’s 1stTr 0.254 0.263 0.140 0.145 0.154 0.160 [0.038]** [0.038]** [0.040]** [0.039]** [0.039]** [0.039]**

Other’s 1st|h -0.140 -0.145 -0.047 -0.051 -0.059 -0.063 [0.037]** [0.037]** [0.038] [0.038] [0.037] [0.037]

Delta 120.273 87.961 125.579 95.171 [11.678]** [15.208]** [29.635]** [30.876]**

D70 7.384 4.918 5.520 3.234 5.735 3.433 [1.800]** [2.007]* [1.657]** [1.839] [1.655]** [1.837]

D120 16.638 16.607 12.686 12.797 13.180 13.281 [2.051]** [2.041]** [1.943]** [1.939]** [1.933]** [1.928]**

Round 0.286 -14.770 -0.123 -14.646 -0.087 -14.583 [0.107]** [4.085]** [0.105] [3.798]** [0.104] [3.788]**

D70*Varinc 0.073 0.072 0.069 0.068 0.069 0.068 [0.012]** [0.012]** [0.011]** [0.011]** [0.011]** [0.011]**

D120*Varinc 0.023 0.023 0.027 0.027 0.027 0.026 [0.014] [0.014] [0.013]* [0.013]* [0.013]* [0.013]*

Varinc 0.116 0.117 0.114 0.115 0.114 0.115 [0.010]** [0.010]** [0.009]** [0.009]** [0.009]** [0.009]**

Round* Equal 0.402 0.393 0.394 [0.220] [0.198]* [0.199]*

Round*Female -0.948 -0.330 -0.378 [0.209]** [0.216] [0.214]

Round*Invest 0.014 0.003 0.004 [0.005]** [0.005] [0.005]

Round*Delta 16.134 15.957 15.903 [4.590]** [4.258]** [4.248]**

Constant -94.776 -64.203 -0.622 1.263 -99.201 -71.437 [9.987]** [13.151]** [2.408] [2.457] [25.432]** [26.553]**

Observations 4112 4112 4112 4112 4112 4112 R-squared 0.26 0.27 0.24 0.24 Number of unique identifier for each individual: 94 Standard errors in brackets Bold means significance at 1% & Gray significance at 5%. Invest & other’s inv are the investment answers for individual & his partner; D70 & D120 are dummies for fixed income of 70 & 120; Varinc is 0 or 200 (h); Round is round number within match; Other’s 1st & Other’s 1st|h is the 1st transfer made by other within a match & interaction with a dummy for the other being high at the time.

Table 6 - Transfer Regressions: transfer given when high Transfer given

when h (1) (2) (3) (4) (5) (6)

ols ols fe fe re re

Invest -0.198 -0.279 -0.259 -0.284 [0.045]** [0.056]** [0.104]* [0.106]**

Other’s Inv -0.173 -0.167 -0.057 -0.057 -0.073 -0.068 [0.045]** [0.045]** [0.048] [0.048] [0.047] [0.046]

Female dummy -15.079 -8.930 -11.883 -8.963 [1.942]** [2.507]** [4.914]* [4.993]

Female other 0.332 -0.511 0.872 0.872 0.820 0.782 [1.911] [1.923] [1.914] [1.914] [1.887] [1.878]

Other’s 1stTr 0.363 0.369 0.216 0.216 0.234 0.238 [0.070]** [0.070]** [0.068]** [0.068]** [0.067]** [0.067]**

Other’s 1stTr|h -0.172 -0.163 -0.048 -0.048 -0.072 -0.066 [0.068]* [0.068]* [0.065] [0.065] [0.064] [0.064]

Delta 191.769 146.743 189.769 138.964 [21.332]** [27.875]** [48.677]** [50.260]**

D70 21.512 17.956 14.032 14.032 18.321 14.513 [2.333]** [2.836]** [2.471]** [2.471]** [2.041]** [2.463]**

D120 22.751 22.614 20.073 20.073 20.393 20.364 [2.738]** [2.720]** [2.477]** [2.477]** [2.466]** [2.454]**

Round 0.447 -21.270 -25.092 -25.092 -0.127 -24.496 [0.196]* [7.501]** [6.600]** [6.600]** [0.180] [6.573]**

Round* Equal 0.461 0.588 0.588 0.581 [0.401] [0.341] [0.341] [0.341]

Round* Female -1.560 -0.727 -0.727 -0.795 [0.384]** [0.372] [0.372] [0.368]*

Round* Invest 0.026 0.008 0.008 0.010 [0.009]** [0.008] [0.008] [0.008]

Round* Delta 23.114 27.253 27.253 26.624 [8.417]** [7.393]** [7.393]** [7.364]**

Constant -120.345 -76.995 29.368 29.368 -119.484 -72.681 [18.176]** [24.124]** [3.828]** [3.828]** [41.762]** [43.245]

Observations 2056 2056 2056 2056 2056 2056 R-squared 0.17 0.18 0.07 0.07 Number of unique identifier for each individual: 94 Standard errors in brackets Bold indicates significance at 1% and Gray indicates significance at 5%. Invest and other’s invest are the answer to initial investment question for individual and his partner; D70 and D120 are dummies for fixed income of 70 and 120 respectively; Varinc is 0 or 200 (h); Round is the round number within a match; Other’s 1st and Other’s 1st|h is the 1st transfer made by the other within a match and its interaction with a dummy that takes value 1 if the other was high at the time.

Table 7 - Transfer Regressions: transfer given when low (1) (2) (3) (4) (5) (6) transfer

given transfer given

transfer given

transfer given

transfer given

transfer given

Invest 0.007 -0.011 -0.007 0.000 [0.017] [0.021] [0.042] [0.043]

Othr’s inv 0.034 0.033 0.046 0.045 0.042 0.042 [0.017]* [0.017] [0.017]** [0.017]** [0.017]* [0.017]*

Female dummy -2.630 -1.130 -1.856 -1.924 [0.732]** [0.943] [2.019] [2.041]

Female other 3.080 2.987 2.184 2.226 2.213 2.273 [0.733]** [0.740]** [0.699]** [0.698]** [0.688]** [0.688]**

Other 1st tr 0.161 0.169 0.104 0.108 0.108 0.113 [0.026]** [0.026]** [0.024]** [0.024]** [0.024]** [0.024]**

Oth 1st tr|h -0.114 -0.122 -0.065 -0.070 -0.068 -0.073 [0.025]** [0.025]** [0.023]** [0.023]** [0.023]** [0.023]**

Delta 46.812 25.649 44.158 30.302 [8.069]** [10.482]* [19.975]* [20.421]

D70 7.746 6.204 5.894 4.879 6.042 4.991 [0.889]** [1.081]** [0.732]** [0.876]** [0.729]** [0.875]**

D120 14.174 14.201 9.714 9.816 10.106 10.216 [1.027]** [1.023]** [0.887]** [0.885]** [0.879]** [0.878]**

round ID 0.025 -9.581 -0.123 -6.432 -0.114 -6.683 [0.074] [2.816]** [0.064] [2.315]** [0.064] [2.309]**

round*equal 0.258 0.183 0.189 [0.152] [0.120] [0.121]

Round* sex -0.365 0.091 0.061 [0.143]* [0.131] [0.130]

Round*invest 0.006 -0.002 -0.002 [0.003] [0.003] [0.003]

Round*delta 10.373 7.011 7.279 [3.166]** [2.596]** [2.590]**

Constant -42.860 -22.997 -0.449 0.404 -37.443 -24.932 [6.863]** [9.030]* [1.394] [1.426] [17.133]* [17.543]

Observations 2056 2056 2056 2056 2056 2056 R-squared 0.12 0.13 0.07 0.08 Number of unique identifier for each individual: 94 Standard errors in brackets Bold indicates significance at 1% and Gray indicates significance at 5%. Invest and other’s invest are the answer to initial investment question for individual and his partner; D70 and D120 are dummies for fixed income of 70 and 120 respectively; Varinc is 0 or 200 (h); Other’s 1st and Other’s 1st|h is the 1st transfer made by the other within a match and its interaction with a dummy that takes value 1 if the other was high at the time.

Table 8 - Transfer and Beliefs All transfers Transfers when high (1) (2) (3) (4) (5) (6) ols fe re ols fe re Investment -0.203 -0.154 -0.443 -0.409

[0.061]** [0.081] [0.119]** [0.151]**

Other’s Inv -0.067 -0.003 -0.054 -0.153 -0.050 -0.107 [0.045] [0.078] [0.058] [0.081] [0.126] [0.100]

Female dummy -8.848 -7.922 -13.340 -15.821 [2.860]** [3.718]* [5.268]* [6.961]*

Female other 1.878 1.379 1.367 0.906 -1.019 0.635 [2.015] [3.323] [2.538] [3.729] [5.381] [4.368]

Other’s 1stTr 0.231 0.222 0.242 0.315 0.197 0.297 [0.091]* [0.129] [0.108]* [0.156]* [0.212] [0.181]

Other’s 1st|h -0.198 -0.127 -0.174 -0.219 0.113 -0.067 [0.088]* [0.125] [0.104] [0.151] [0.212] [0.178]

Delta 89.135 81.385 147.929 98.947 [28.434]** [36.645]* [52.469]** [68.659] D70 3.016 -3.956 0.282 15.159 20.419 17.963 [4.314] [4.386] [4.092] [6.385]* [6.059]** [5.563]** D120 13.547 3.281 9.421 19.534 23.229 22.420 [3.274]** [4.667] [3.719]* [4.537]** [7.207]** [5.583]** Belief Diff 4.125 7.590 5.383 7.410 11.956 10.258 [1.064]** [1.761]** [1.348]** [1.949]** [3.118]** [2.431]** round -8.533 -8.070 -8.439 -9.205 -14.895 -13.075 [6.002] [5.909] [5.734] [11.105] [9.912] [9.574] Round* Equal 1.208 2.124 1.847 2.804 -1.168 1.179

[2.199] [1.998] [1.996] [4.092] [3.635] [3.469] Round*Female 0.280 -0.153 -0.012 0.203 0.798 0.646

[0.637] [0.644] [0.622] [1.194] [1.078] [1.044] Round*Invest 0.043 0.002 0.015 0.068 0.013 0.025

[0.012]** [0.012] [0.012] [0.024]** [0.021] [0.020] Round*Delta 5.645 8.146 7.590 3.879 14.096 11.149 [6.817] [6.702] [6.510] [12.530] [11.169] [10.800] D70*Varinc 0.078 0.097 0.086

[0.025]** [0.024]** [0.023]** D120*Varinc 0.022 0.043 0.036

[0.022] [0.021]* [0.020] Varinc 0.092 0.085 0.088

[0.016]** [0.015]** [0.014]** Constant -53.205 7.234 -49.018 -62.044 22.029 -25.966 [24.651]* [6.319] [31.609] [45.676] [9.945]* [59.258] Observations 936 936 936 468 468 468 R-squared 0.25 0.24 0.20 0.17 Number of unique identifier for each individual: 94 Standard errors in brackets Bold means significance at 1% & Gray significance at 5%. Invest & other’s inv are the investment answers for individual & his partner; D70 & D120 are dummies for fixed income of 70 & 120; Varinc is 0 or 200 (h); Round is round number within match; Other’s 1st & Other’s 1st|h is the 1st transfer made by other within a match & interaction with a dummy for the other being high at the time.