SECRET SANTA REVEALS THE SECRET SIDE OF GIVING
BRIAN DUNCAN*
This article shows how a secret Santa gift exchange offers unique insights into the
nature of generosity and charitable giving. In a dictator experiment modified with
features similar to a secret Santa gift exchange, I find that individuals contribute
less when their gifts are allocated such that each person gives to fewer recipients.
The results are inconsistent with both altruism and warm glow, suggesting that
players are motivated by something in addition to these conventional models of
generosity. Several alternative models of generosity are shown to be consistent
with the experimental findings, all of which imply that, in addition to any positive
externalities, giving can also carry a negative externality. (JEL H41, C92, D62)
I.
INTRODUCTION
generosity—questions that conventional
models of generosity cannot answer. For example, why would a secret Santa gift exchange
reduce holiday spending, and if it does, why
would a reduction in holiday spending benefit
participants?
A secret Santa gift exchange is essentially
a cooperative gift-giving agreement. In conventional models of generosity, cooperation
benefits participants because giving carries
a positive externality. This externality occurs
because giving brings enjoyment to the giver,
the receiver, and (possibly) third parties. For
example, when a grandmother gives her grandchild a new bicycle, both benefit. In addition,
the child’s parents may benefit from their child
receiving a bike that they did not have to pay
for. In models with positive externalities, cooperation makes everyone better off by increasing the total amount of giving. Conversely,
cooperation in a secret Santa gift exchange
makes everyone better off by decreasing the
total amount of giving. By doing so, a secret
Santa gift exchange may reveal a hidden aspect
of giving: negative externalities.
The idea that giving could be associated
with a negative externality may seem somewhat unphilanthropic. However, this article
shows that several reasonable philanthropic
assumptions, such as impact philanthropy
and social comparison, unavoidably lead to
negative gift externalities. For example, the
At Christmas, large families and groups of
friends often organize secret Santa gift
exchanges in which each participant gives
and receives one gift rather than giving and
receiving gifts from everyone. Participants
typically draw names from a hat to assign each
person a secret Santa. Organizers claim that
a secret Santa gift exchange will benefit participants in two ways. The first is obvious: buying and wrapping one large gift is easier than
buying and wrapping several smaller gifts.
This benefit suggests that a secret Santa gift
exchange lowers the cost of gift giving, and
so we would expect to see a corresponding
increase in holiday spending. However, organizers also claim that a secret Santa gift
exchange will save participants’ money, while
allowing them to give and receive more meaningful gifts. This benefit suggests that a secret
Santa gift exchange will reduce holiday spending, as a participant who would otherwise give
ten gifts worth $12 each will be inclined to give
one gift worth something less than $120.1
While this behavior seems reasonable, it raises
some revealing questions about the nature of
*I thank Orathai Chitasaranachai, R. Kaj Gittings,
and Benjama Witoonchart for their excellent research
assistance.
Duncan: Associate Professor, Department of Economics,
University of Colorado Denver, Campus Box 181,
Denver, CO 80217-3364. Phone 1-303-556-6763, Fax
1-303-556-3547, E-mail [email protected]
1. In fact, organizers often ensure this result by placing a limit on the amount of money each participant may
spend on a gift.
ABBREVIATION
OLS: Ordinary Least Squares
1
Economic Inquiry
(ISSN 1465-7295)
doi:10.1111/j.1465-7295.2008.00145.x
2008 Western Economic Association International
2
ECONOMIC INQUIRY
grandmother’s gift of a new bicycle might
diminish the impact of the parent’s gift. One
cousin might give a larger gift to avoid being
labeled as the cousin who gives the smallest
gift. A husband might buy an expensive gift
for his wife fearing that his wife will buy
him an expensive gift. All these motives imply
a negative gift externality.
For the purposes of this article, the important feature of a secret Santa gift exchange is
that it concentrates each person’s gift rather
than spreading it around. This gift concentration is unique, in that it is done without eliminating recipients. For example, agreeing to
give Christmas presents only to the youngest
children in a family would concentrate gifts
but not in the same way as a secret Santa gift
exchange. Rather, a secret Santa gift exchange
concentrates gifts not by eliminating recipients
but by restricting the way gifts are allocated
among recipients. In fact, the idea of restricting
the way gifts are allocated among a group of
recipients is not limited to the secret Santa gift
exchange. It is also seen in common fund-raising strategies, such as a children’s organization
that allows a donor to sponsor an individual
child rather than contribute to a general fund.
Setting aside the possible motives for this fundraising strategy, sponsoring children raises an
interesting philanthropic question. If, at the
end of the day, 1,000 needy children are fed,
does a donor feel more satisfied if he or she
fed one child or if he or she provided each
of these thousand children with a single grain
of rice? Models traditionally used by economists to explain charitable giving do not adequately address this question. For example,
altruism suggests that donors contribute
because they value the welfare of children.
Warm glow suggests that donors contribute
because they value the act of giving. Holding
constant the welfare of the children and the size
of each donor’s gift, neither motive explains
why a donor would care how his or her contribution is specifically allocated among recipients. However, both the secret Santa gift
exchange and the common fund-raising strategies suggest that some donors view having
a large impact on a few recipients differently
than having a small impact on many.
To address these questions, this article
presents the results of a modified dictator
game with a unique payoff structure designed
specifically to determine what effect, if any,
targeting gifts at fewer recipients has on aver-
age giving. The players’ behavior strongly suggests that targeting gifts at fewer recipients
reduces average giving. Although the experimental results do not rule out altruism and
warm glow as important charitable motives,
they do suggest that something in addition
to these traditional models must also be motivating players to give. Furthermore, this additional motive is consistent with models that
imply a negative gift externality.
II.
CONCENTRATING GIFTS VERSUS
TARGETING GIFTS
Gifts are said to be concentrated whenever
a donor gives to fewer recipients. The simplest
way to concentrate gifts is to restrict the group
of recipients. However, neither a secret Santa
gift exchange nor sponsoring children necessarily excludes recipients. Instead, these examples concentrate gifts by targeting them at
specific recipients. That is, gifts are said to
be targeted when (a) each donor gives to fewer
recipients and (b) each recipient receives from
fewer donors. For example, the question
above asked how a donor would feel about
feeding one child versus partially feeding
many, holding constant the total amount of
food going to each child. This question implicitly asks about the net effect of (a) and (b). An
example of concentrating gifts, effect (a) without (b), would be to give half as many children
twice as much food. In this case, neither the
total amount of food nor the average amount
of food going to each child has changed; the
food is simply concentrated among fewer
recipients.2 Concentrating gifts in this fashion
would have no effect on a warm glow philanthropist, who cares only about the total size of
his or her gift.3 However, an altruist, who
cares about the total utility of a group of homogeneous recipients, would prefer to equalize
2. This, of course, includes children who do not
receive any food in the average. The alternative would
be to say that the average gift doubles when half as many
children receive twice as much food. While it would be
unreasonable to assume that an altruist could change
the size of the recipient group simply by ignoring some
of them, this assumption may not be unreasonable in other
models of philanthropy, particularly those in which
donors care about perceived gratitude or the impact of
their gifts.
3. Rather than caring about the total amount given,
a warm glow philanthropist might instead care about
the amount of each individual gift. Section V discusses
how donors with such alternate philanthropic motives
would view targeted giving.
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
the marginal utility of food across recipients.
Therefore, for an altruist, concentrating gifts
would not be a desirable outcome.4
This article refers to (a) as concentrating
gifts and to the combined effect of (a) and
(b) as targeting gifts. Whereas a single donor
can independently concentrate his or her gift,
targeting gifts requires coordination among
donors or requires a third party to impose this
coordination. Moreover, a targeted arrangement can be constructed such that if each
donor gives the same amount when gifts are
targeted compared to when gifts are spread
around, then each recipient will receive the
same amount when gifts are targeted compared to when gifts are spread around. Therefore, by combining effects (a) and (b),
a targeted allocation nets out other confounding effects, such as group size and the need of
recipients. This allows us to determine
whether donors view having a large impact
on a few recipients differently than having
a small impact on many, without having to
change the welfare of any recipient.
III. EXPERIMENTAL DESIGN
Subjects who participated in the experiment
were recruited from undergraduate courses at
the University of Colorado Denver in the
spring semester of 2001. Subjects were told that
they would play a game, lasting approximately
1 hour, in which they would earn money, paid
to them in cash at the end of the game. How
much money they would earn, the participants
were told, would depend on the decisions they
and the other players make during the game.
Players were not paid a show-up fee. A total
of 96 subjects participated in eight sessions,
each containing 12 players and 8 rounds, totaling 768 decision observations. The participants
earned $10.46 on average.
At the start of each session, the players were
given a set of instructions and the rules of the
4. This result relies on general assumptions regarding
the recipient’s utility function. If, for example, the recipient’s utility is continuous and strictly concave in food,
then maximizing total utility implies equalizing the marginal utility of food across recipients. This assumption
would be violated if a minimal amount of food is required
for survival and if the donors’ contributions can push
recipients across this threshold. In this case, equalizing
the marginal utility of food across recipients could result
in starving all recipients to death. However, the focus of
this article is not on state-dependent utility, and so we will
assume that utility is continuous and strictly concave.
3
game they were going to play.5 The instructions and rules of the game were read aloud,
and the players were allowed to ask questions.
Players were told that they would play the
game for eight rounds. In each round, players
were given 100 tokens that they could ‘‘hold’’
or ‘‘pass.’’ Players were allowed to hold all
their tokens, hold some and pass some, or pass
all their tokens. At the end of each round,
tokens were converted into points in the following way: each token a player held earned
him or her one point; each token a player
passed became two points, distributed to other
players in the group. At the end of the experiment, players were paid one penny for each
point they earned. In all treatment groups,
the self-interest Nash equilibrium was for
every player to hold all their tokens, while
the cooperative equilibrium was for every
player to pass all their tokens.
Deviations from the Standard Dictator Game
In this experiment, a player’s passed tokens
were doubled into points, which were then
equally divided among one, three, or five
recipients, depending on the treatment group.6
A player never received any of the points generated from his or her own passed tokens,
meaning that it costs a player one point to pass
one token.7 However, in all sessions, passed
tokens were doubled into points, meaning that
it costs a player one point to give two points.
The new and unique feature of this experiment
is how points were distributed to recipients.
The distribution of passed tokens to recipients
was explained to the players by having them
think of 12 positions around a circle, like
the numbers on the face of a watch. The ‘‘rules
of the game’’ showed players several examples
of one of the three point distribution circles
depicted in Figure 1. Each position on the circle represents a different player. The points
generated from one player’s passed tokens
were equally divided among the recipients
5. The instruction sheet and rules of the game can be
downloaded at http://www.econ.cudenver.edu/bduncan.
6. There were three sessions each of the one- and fiverecipient treatments and two sessions of the three-recipient
treatment. Each player participated in only one treatment
group.
7. Isaac and Walker (1988) found that players’ contributions were sensitive to the marginal return they received
from contributions to the group investment. To control
for this effect, the experiment reported in this study holds
constant the marginal return from passed tokens at zero.
4
ECONOMIC INQUIRY
FIGURE 1
The Point Distribution Circles for the Three Treatment Groups
Three Recipients
Five Recipients
Points from position a’s
passed tokens are equally
divided between positions
b, c, and d.
Points from position a’s
passed tokens are equally
divided between positions b,
c, d, e, and f.
One Recipient
Points from position a’s
passed tokens are given to
position b.
a
l
k
l
c
e
i
f
g
Position “a” receives the
points from the passed tokens
of position l.
l
b
k
d
j
h
a
a
b
k
c
d
j
e
i
h
b
f
c
d
j
e
i
h
f
g
g
Position “a” receives onethird of the points from the
passed tokens of positions j, k,
and l.
Position “a” receives one-fifth
of the points from the passed
tokens of positions h, i, j, k,
and l.
Notes: Each player participated in one of the three treatment groups depicted above. In addition to being shown one of
the figures above, players were told that (a) ‘‘The computer randomly places players in new positions after each round,’’ (b)
‘‘In a given round, the players that split your ‘passed’ tokens are never the same players that ‘pass’ tokens to you,’’ and (c)
‘‘you will never be told the identity of the players that split your ‘passed’ tokens, not will they be told your identity.’’
assigned to the next one, three, or five positions
clockwise, depending on which treatment
group the subject participated in. Players were
told that a computer randomly placed players
in new positions at the beginning of each
round.8 It was also pointed out that, in a given
round, players never passed and received
tokens to and from the same player. Thus,
the dictator is a recipient but not a recipient
of any of the players he or she rules over in
a given round. Finally, players were not
allowed to communicate and were not told
the identity of the players who split their
passed tokens or who passed tokens to them.9
This experiment deviates from the typical
dictator game in several important ways.
8. Randomizing groups in repeated games reduces the
incentive for reputation building.
9. Players were not asked to give their name and were
identified only by a randomly assigned identification number. To ensure anonymity, players put their decisions in an
envelope that was passed to a research assistant outside
the room. The person inside the room was not allowed
to see the choices the subjects made, and the person outside the room was not allowed to see the subjects.
These deviations were designed to determine
how targeting gifts at smaller groups of recipients affects giving while attempting to hold
constant other factors that might affect giving,
such as strategic play, group size, the need of
recipients, and the marginal return from
passed tokens. Furthermore, the deviations
were designed such that the conventional
models of generosity would predict either no
difference in giving between the different treatments or that giving will increase as gifts are
targeted.
The first deviation is the doubling of a dictator’s passed tokens into points.10 Doubling
tokens into points mimics charitable giving in
the sense that tokens become more valuable
to recipients than to dictators. Second, the
typical dictator game has one dictator and
one recipient. This experiment has several
10. Doubling passed tokens into points sets the relative price of giving at 0.5. This price was held constant
across all treatment groups. Andreoni and Miller (2002)
ran several treatments of the dictator game in which the
relative price of giving ranged from 0.25 to 3 and found
that the players responded rationally to changes in price.
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
dictators and several recipients. This design
feature controls for the need of the recipient
and allows for the possibility of a symmetric
equilibrium. For example, if every dictator
passes the same number of tokens (say 20
tokens), then every player would receive the
same payoff (120 points) regardless of the
treatment group. Therefore, from a dictator’s
point of view, as the number of recipients
increases, the need of the recipients does
not. Third, in this experiment, dictators are
also recipients. Being both a dictator and
a recipient complicates matters because it
introduces the possibility of strategic play.
Strategic play is minimized by anonymity
and randomizing positions on the payoff circle
and is accounted for by examining first- and
last-round play, as well as by regression
analysis.
IV. EXPERIMENTAL RESULTS
A. Basic Patterns
Overall, players passed an average of 33.4%
of their endowment to other players. They
passed more, 39.1%, in the first round than
they did in the last round, 23.9%. Both the
level of contributions and the pattern of contribution decay are consistent with other studies such as Isaac and Walker (1988), Forsythe
et al. (1994), Cason and Mui (1997), Bohnet
and Frey (1999), and Andreoni and Miller
(2002).
The first group of three columns in Table 1
lists the average percent of endowment passed
to other players per round by the one-, three-,
and five-recipient treatment groups. Figure 2
graphs this information. Players who passed
tokens to one other player passed, on average,
23.9% of their tokens. This result is consistent
with other dictator game studies. For example,
in the two treatments in which Andreoni and
Miller’s (2002) dictators had their tokens doubled into points, they passed an average of
32.3% and 30.3% of their endowment.11
11. The first round of the one-recipient treatment
group differs from Andreoni and Miller’s (2002) dictator
experiment in that, in this experiment, dictators were also
recipients. Being a recipient introduces the possibility of
strategic play, which is discussed below in the Strategies
and Regression Analysis section. However, the fact that
players in this experiment passed the same amount as players in a pure dictator game suggests that being a recipient
had little effect on dictators.
5
Players who passed tokens to three and five
other players passed, on average, 36.7% and
40.7% of their tokens, respectively. This result suggests that players give less when their
contributions are targeted at fewer recipients.
The biggest difference in contributions was
between the one- and three-recipient treatment groups at 12.8%. The difference in
contributions between the three- and the fiverecipient treatment groups, 4%, was smaller.
Combined, the difference in contributions
between the one- and five-recipient treatment
groups was 16.8%. This pattern of results held
in the first round, last round, and all rounds in
between.
The second and third groups of columns in
Table 1 separate average contributions by
gender. Recently, several economists have
studied gender differences in altruism.12 There
seems to be no simple answer to the question,
‘‘are women more altruistic than men?’’ Eckel
and Grossman (1998, 2006) find that all female
groups are more altruistic than groups containing only men. On the other hand, Bolton
and Katok (1995) find no significant differences between the altruism of men and women in
mixed groups. However, in Bolton and
Katok’s experiments, the price of contributions was 1. Andreoni and Vesterlund (2001)
vary the price of contributions and found that
at low prices, men contribute more than
women, but at higher prices, women contribute more than men13 Finally, using survey
data from the Independent Sector’s Giving
and Volunteering Survey, Andreoni, Brown,
and Rischall (2003) could not reject the
hypothesis that men and women have the
same demand function for altruism, but they
found other differences between men and
women. For example, Andreoni, Brown,
and Rischall found that men tend to give large
gifts to a few organizations, while women tend
to give small gifts to many organizations.
The recruiting for the experiment reported
in this study placed no emphasis on gender. Of
the 96 participants, 46 were women and 50
were men. Figure 3 graphs the average percent
of endowment passed to recipients by round.
Panels A and B graph the contributions of
12. See Brown-Kruse and Hummels (1993) and Eckel
and Grossman (1998) for a review of gender difference in
laboratory experiments.
13. In fact, Andreoni and Vesterlund (2001) found
that the male and female demand for altruism cross near
the price of 1.
(4.72)
(4.81)
(5.77)
(5.94)
(4.84)
(4.63)
(4.77)
(4.75)
23.90 (1.80)
12.83*** (3.01)
30.36
29.69
29.89
27.94
21.17
18.08
18.00
16.03
(6.77)
(7.62)
(7.09)
(7.53)
(6.31)
(6.52)
(7.56)
(7.34)
36.73 (2.51)
3.99 (3.22)
16.82*** (2.71)
9.01 (8.35)
43.71
46.46
41.83
36.63
33.50
34.79
31.88
25.04
Three
(5.61)
(5.25)
(6.11)
(5.51)
(5.34)
(6.21)
(6.06)
(5.70)
6.00 (9.2)
15.01** (7.42)
40.72 (2.03)
44.83
46.94
47.83
41.57
40.20
40.47
32.83
31.04
Five
(7.16)
(7.11)
(8.31)
(9.21)
(7.90)
(7.67)
(7.02)
(6.08)
29.89 (2.71)
9.29** (4.24)
36.53
36.68
35.63
38.47
28.79
24.47
24.74
13.79
One
(9.19)
(10.32)
(9.34)
(9.80)
(8.19)
(8.23)
(10.44)
(9.49)
39.18 (3.33)
8.42* (4.64)
17.71*** (4.19)
8.8 (10.85)
46.60
53.33
44.60
37.60
35.27
40.33
33.00
22.67
Three
Recipients
Recipients
12.18 (13.29)
21.05*(10.80)
47.60 (3.24)
a
(9.46)
(8.49)
(8.45)
(8.98)
(8.36)
(10.37)
(10.61)
(9.31)
Five
46.75
54.13
54.68
48.67
52.14
48.44
41.13
34.84
Notes: Of the 96 participants, 50 were male and 46 were female. Standard errors are given in parentheses.
The sum equals the difference between the one- and five-recipient sessions.
Statistically significant at the ***99%, **95%, and *90% confidence levels.
Round
1
2
3
4
5
6
7
8
Last round
Difference
Suma
All rounds
Difference
Suma
One
Male Participants
All Participants
23.47
21.88
23.47
16.18
12.65
10.94
10.47
18.53
(5.74)
(6.04)
(7.90)
(6.35)
(4.62)
(4.37)
(6.05)
(7.57)
One
17.20 (2.18)
15.45*** (4.04)
TABLE 1
Percent of Endowment Contributed to Recipients per Round
(10.03)
(10.37)
(11.28)
(12.42)
(10.39)
(10.56)
(10.93)
(12.15)
32.65 (3.74)
2.56 (4.50)
18.01*** (3.37)
10.47 (13.63)
38.89
35.00
37.22
35.00
30.56
25.56
30.00
29.00
Three
Recipients
Female Participants
(6.90)
(6.47)
(8.68)
(6.78)
(6.28)
(7.43)
(6.74)
(7.21)
1.00 (13.46)
9.47 (10.48)
35.21 (2.50)
43.30
41.20
42.35
35.90
30.65
34.10
26.20
28.00
Five
6
ECONOMIC INQUIRY
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
7
FIGURE 2
Average Percent of Endowment Passed to Other Players per Round
Note: Standard errors are given in parentheses.
men and women, respectively, in each treatment group. Overall, men passed 38.3% of
their endowment and women passed 28.1%14
In fact, men, on average, contributed more
than women in all treatments, although the
difference was not statistically significant for
the three-recipient treatment groups. Both
men and women contributed less when their
contributions were targeted at fewer recipients.
For men, moving from one to three recipients
had roughly the same effect on contributions
as moving from three to five recipients. For
women, however, moving from one to three
recipients had a large effect on their contributions, 15.5 percentage points, but moving from
three to five recipients had a relatively small
effect on their contributions, 2.6 percentage
points. However, in the end, moving from
one to five recipients had virtually the same
effect on the contributions of men and women.
Therefore, the experimental evidence does not
suggest that women are any more or less influenced by targeting gifts than are men.
Table 2 lists the percent of contributions
that were equal to 0% and 100% of the player’s
endowment, by treatment groups. Out of 768
opportunities, players decided to pass none of
their endowment, the self-interest Nash equilibrium, 26.7% of the time, while they decided
14. The average contribution by men was higher than
that by women because men gave more in earlier rounds.
In the final round, men and women contributed equally.
to pass all their endowment, the cooperative
equilibrium, 9.8% of the time. Players who
passed tokens to one other player passed nothing 38.5% of the time. Players who passed
tokens to three or five other players passed
nothing 26.6% and 14.9% of the time, respectively. On the other hand, players who passed
tokens to one other player passed all their
endowment 3.1% of the time. Players who
passed tokens to three or five other players
passed everything 12.5% and 14.6% of the
time. Therefore, the contributions of 0% and
100% of the player’s endowment follow the
same pattern as the average contributions.
In fact, in the final round, 61.1% of players
in the one-recipient treatment passed zero
tokens, compared to 25% of players in the
five-recipient treatment. This suggests that
players are more likely to follow their payoff-dominated strategy of passing zero tokens
when no one else can give to their recipients.
B. Strategies and Regression Analysis
In models of philanthropy, donors contribute to recipients. In economic experiments,
players contribute to other players. Being both
a donor and a recipient in a multiround game
introduces the possibility of strategic play.
Perhaps receiving more in an early round
encourages a player to give more in a later
round (Dufenberg et al. 2001; Fischbacher,
Gächter, and Fehr 2001). Although strategic
8
ECONOMIC INQUIRY
FIGURE 3
Average Number of Passed Tokens per Round, by Gender
Note: Standard errors are given in parentheses.
play may be part of secret Santa gift exchange,
this article is concerned with how targeting
gifts influences the amount given. For this reason, the experiment presented in this article
includes controls to mitigate player strategies.
For example, players are randomly grouped
after each round to minimize the incentive
for reputation building. In addition, the experimental results hold in the first round, where
players could not have been affected by other
players’ strategies; the last round, where players knew that their strategies could not affect
other players; and all rounds in between. Furthermore, for a strategy to bias the results, it
must vary systematically among the three
treatment groups. While there is no reason
to believe that strategies, in general, would
vary between the one-, three-, and five-recipient groups, there is a specific type of player
reciprocity that could. Controlling for this
type of reciprocity does not affect the conclusions drawn from the experiment.
Direct reciprocity is when someone is generous to you, and so you reward that person.
Indirect reciprocity is when someone is generous to you, and so you reward a third person
(typically because you are not able to reward the
person who was generous to you). Dufenberg
et al. (2001) find that players in indirect reciprocity treatments behave similar to players in
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
9
TABLE 2
Percent of Contributions Equal to 0% or 100% of the Player’s Endowment
One
Round 1
Difference
Suma
Round 8
Difference
Suma
All rounds
Difference
Suma
19.4
6.9
11.1
61.1
6.9*
36.1***
38.5
12.0***
23.6***
Contributed 0%
Contributed 100%
Recipients
Recipients
Three
(6.7)
12.5
(9.9)
4.2
(8.2)
(8.2)
54.2
(13.2) 29.2**
(11.0)
(2.9)
26.6
(4.4) 11.6***
(3.6)
Five
(6.9)
(8.0)
8.3 (4.7)
(10.4)
(12.3)
25.0 (7.3)
(3.2)
(3.7)
14.9 (2.1)
One
2.8
13.9*
13.9**
5.6
6.9
5.6
3.1
9.4***
11.5***
(2.8)
(7.2)
(6.9)
(3.9)
(7.4)
(6.6)
(1.0)
(2.3)
(2.3)
Three
Five
16.7 (7.8)
0.0 (10.0)
16.7 (6.3)
12.5 (6.9)
1.4 (8.6)
11.1 (5.3)
12.5 (2.4)
2.1 (3.2)
14.6 (2.1)
Note: Standard errors are given in parentheses.
The sum equals the difference between the one- and five-recipient sessions.
Statistically significant at the ***99%, **95%, and *90% confidence levels.
a
direct reciprocity treatments. Direct and indirect reciprocity become a strategy whenever
one player tries to use reciprocity to elicit
greater contributions from other players.
For example, consider a class of reaction functions in which player i’s contribution in round
t is a function of his or her payoff in round
t 1, that is, git 5 f(rit1). Now consider
two sessions of a simplified version of the experiment presented in this article. There are
four players. The payoffs generated from the
first two players’ contributions in round t are
r1t and r2t. In the first session, these returns
are split equally between Players 3 and 4,
and in the second session, Player 1 gives to
Player 3, while Player 2 gives to Player 4.
Finally, suppose that each player’s reaction
function, f, is concave, as shown in Figure 4.
In the fist session, when gifts are spread around,
both Players 3 and 4 receive r and give g~ in the
following round. Total giving by Players 3 and
4 in the following round is 2~
g. In the second
session, when gifts are targeted, Player 3 receives r1t1 and gives g3t in the following round,
while Player 4 receives r2t1 and gives g4t in the
following round. Total giving by Players 3 and
4 in the following round is 2
g, which is less than
2~
g whenever f is concave. In this example, total
giving decreases when gifts are targeted at specific recipients. Although models of reciprocity
can generate negative gift externalities, it is not
required that they do so. In fact, a concave
reaction function (such as the one shown in
Figure 4) can come from a model with either
positive or negative externalities.
A reaction function, f, can influence the
results of the experiment presented in this article if it is strictly concave or strictly convex. In
addition, the reaction function need not be
based solely on the payoffs in the previous
round but may be a function of all previous
payoffs. Table 3 presents marginal effects calculated from two-way censored Tobit regressions designed to control for potential reaction
functions.15,16 The dependent variable in each
regression is the number of tokens passed by
a player in each round. Column (1) displays
the regression that includes dummy variables
for the three- and five-recipient treatment
groups and for each round. The one-recipient
treatment group and Round 1 are the omitted
categories. The estimated marginal effects are
consistent with the basic patterns and suggest
15. The lower censoring point is 0, and the upper censoring point is 100. Standard ordinary least square (OLS)
models (not reported) produce ‘‘session’’ estimates that
have the same sign and significance but are one to three
tokens smaller in magnitude.
16. Ashley, Ball, and Eckel (2003) argue for including
fixed effects in the analysis of public goods experiments.
Although each player makes multiple decisions, including
fixed effects is not feasible because each player participated in a single treatment group. In OLS regressions that
cluster the standard errors at the individual level (not
reported), the five-recipient treatment dummy remains
statistically significant, but the three-recipient treatment
dummy becomes statistically insignificant when demographic controls are included.
10
ECONOMIC INQUIRY
FIGURE 4
Gift Reaction Function
g
f (rit–1)
g4t
g~
g
g3t
r1t–1
r
r2t–1
r
that targeting contributions decreases giving.
Column (2) adds demographic and other controls.17 Older subjects and those currently
employed gave more, while foreign-born subjects gave less, but none of these differences
are statistically significant. White male subjects gave the most. The variable ‘‘Friends’’
represents the number of other players a subject knows and considers a friend.18 Sixty-one
percent of subjects indicated that they considered at least one other player a friend. The
average number of friends was 1.79. As one
might expect, the presence of friends increased
giving—if only slightly—by less than two
tokens. All else equal, a subject in the fiverecipient treatment knew that he or she was
more likely to give to a friend than a subject
in the one-recipient treatment. To control
for this, additional specifications were estimated (not reported) that included interaction
terms between the number of friends and the
treatment dummies.19 These interaction terms
were not statistically significant.
17. Participants completed an exit survey at the end of
the experiment. The exit survey indicated the subject’s randomly assigned player identification number but did not
reveal the player’s name or any other identifying information.
18. Subjects were randomly assigned to a session. As
a result, some subjects knew other subjects.
19. I am grateful to an anonymous referee for this
comment.
Columns (3), (4), and (5) in Table 3 include
controls for a player’s reaction function. The
three controls are lag, sum, and average. Lag
represents the number of points received in the
previous round. Sum represents the total
points received in all previous rounds. Average
represents the average number of points
received in previous rounds. In each case,
the square of the control variable is also
included in the regression. None of the variables included to control for a player’s reaction
function are statistically significant. After controlling for demographic characteristics, number of friends, and potential reaction effects,
all the regressions suggest that players contributed the most in the five-recipient treatment
group and the least in the one-recipient treatment group. Controlling for potential reaction
effects, the results continue to suggest that
players give less when their gifts are targeted
at fewer recipients.
V. MODELS OF GENEROSITY
The experiment reported in this study
placed players in a situation in which they
had no direct financial incentive to pass
tokens. That they did suggests the presence
of some form of generosity, strategic play,
or confusion. There is no reason to believe that
one treatment was more or less confusing than
another, and so their systematic nature makes
it unlikely that confusion can explain the
results. Rerandomizing groups after each
round minimized the incentive for reputations
building, and regression analysis controlled
for other forms of strategic play. Additionally,
the results hold in the first round, the last
round, and all the rounds in between, and
so it is unlikely that reputation effects can
explain the results. This leaves generosity.
Generosity, in an experimental setting, means
that a player is willing to increase another
player’s payoff at some personal cost. It is
important to note that although the cost of
generosity is built into the experiment’s payoff
structure, the motive for generosity is not.
Rather, the motive to be generous, or not, is
something that players bring with them to
the experiment. As a consequence, every
experiment in which one player’s action can
affect another player must consider the
implications of generosity. Competing models
of generosity include altruism, warm glow,
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
11
TABLE 3
Marginal Effects Calculated from Two-Way Censored Tobit Regressions
(1)
Treatment
Three recipients
Five recipients
Round
2
3
4
5
6
7
8
Age (yr)
26–35
36 or older
Friends
Female
Ethnicity
Black
Asian
Other
Foreign born
Employed
Received
Lag
Lag2/1,000
Sum
Sum2/1,000
Average
Average2/1,000
Likelihood ratio
Sample size
(2)
13.87*** (3.20)
19.26*** (2.76)
0.04
1.03
5.84
8.01*
9.22**
13.03***
17.13***
(4.60)
(4.59)
(4.40)
(4.29)
(4.25)
(4.06)
(3.83)
(3)
10.19*** (3.51)
22.18*** (3.20)
(4)
11.15*** (4.28)
24.04*** (4.23)
(5)
8.20** (4.00)
20.23*** (3.94)
8.28** (4.06)
20.28*** (4.02)
0.01
1.17
6.04
8.29*
9.31**
13.42***
17.30***
(4.54)
(4.53)
(4.33)
(4.22)
(4.19)
(3.99)
(3.77)
1.41
6.52
8.33**
8.95**
13.15***
17.04***
(4.51)
(4.30)
(4.20)
(4.19)
(3.97)
(3.77)
2.55
8.52*
11.69**
13.56**
18.15***
22.31***
(4.74)
(4.93)
(5.15)
(5.28)
(5.03)
(4.68)
1.15
5.82
7.75*
8.56**
12.50***
16.27***
(4.52)
(4.33)
(4.26)
(4.24)
(4.04)
(3.81)
0.53
3.06
1.51**
10.97***
(3.49)
(6.42)
(0.58)
(2.35)
1.70
3.81
1.69***
11.29***
(3.71)
(6.89)
(0.63)
(2.51)
0.93
3.63
1.69***
11.57***
(3.79)
(6.87)
(0.62)
(2.52)
0.53
3.44
1.71***
11.64***
(3.81)
(6.86)
(0.63)
(2.52)
11.67***
11.60***
10.55***
0.48
3.74
(4.10)
(3.58)
(3.14)
(3.17)
(2.58)
10.94**
11.85***
9.69***
0.43
3.74
(4.41)
(3.80)
(3.37)
(3.39)
(2.77)
10.86**
11.82***
9.40***
0.15
3.68
(4.42)
(3.80)
(3.41)
(3.41)
(2.77)
10.71**
11.60***
9.38***
0.16
3.63
(4.43)
(3.80)
(3.41)
(3.40)
(2.77)
0.07 (0.09)
0.58 (0.53)
0.02 (0.03)
0.001 (0.033)
77.86
768
122.35
768
111.95
672
111.92
672
0.03 (0.14)
0.31 (0.81)
113.49
672
Notes: The dependent variable is the number of tokens passed by a player in a given round. One recipient, round 1, age
25 or less, male, white, native born, and not working are the omitted groups. ‘‘Friends’’ is the number of other players
a participant knows and considers a friend. ‘‘Lag’’ is the number of points earned from other players in the previous round.
‘‘Sum’’ is the total points earned from other players in previous rounds. ‘‘Average’’ is the average points earned from other
players in previous rounds. Round 1 is excluded from regressions (3), (4), and (5) because the received variables are missing. For these regressions, Round 2 is the omitted group. OLS models produce ‘‘session’’ estimates that have the same sign
and significance but are one to three tokens smaller in magnitude. Fixed-effects regressions are not feasible because each
player participated in only one session type.
Statistically significant at the ***99%, **95%, and *90% confidence levels.
prestige, impact philanthropy, social comparison, and fairness.
A. Altruism and Warm Glow
Economists use a variety of models to
explain why a donor would contribute to
a charitable organization or why an experiment player would pass tokens to another
player. The conventional models of generosity
are altruism and warm glow. To motivate
these models, consider a philanthropist who
values his or her personal consumption, xi,
but also has the opportunity to make a charitable contribution, gi. When a philanthropist
contributes to charity, something must motivate that contribution. In the model of altruism, philanthropists contribute motivated by
their desire to consume a nonrival, nonexcludP
able public good G, where G 5 i gi . The
12
ECONOMIC INQUIRY
altruist’s utility function, written ui(xi,G),
implies that individual contributions are interdependent, in that giving by one altruist
directly increases the utility of other altruists.
Gift interdependency in the altruist model
leads to many well-established public goods
phenomena, such as free riding and crowding
out (Bergstrom, Blume, and Varian 1986;
Roberts 1984; Warr 1982). It also gives altruists an incentive to cooperate with each other.
Cooperation among altruists leads to an
increase in contributions because in its
absence, altruists fail to account for positive
gift externalities (Stiglitz 1987).
Conversely, warm glow philanthropists
contribute motivated by the personal satisfaction the act of giving brings or, equivalently,
because giving alleviates social guilt
(Andreoni 1990; Menchik and Weisbrod
1981). The warm glow philanthropist’s utility
function, written ui(xi,gi), implies that contributions are independent, in that giving by one
philanthropist does not affect the utility of
other philanthropists. As a result, a warm
glow philanthropist cannot free ride off of
the gifts of others and has no incentive to
cooperate with other philanthropists.
Neither altruism nor warm glow can
explain why targeting gifts would decrease giving. In fact, targeting gifts should have no
effect on a warm glow philanthropist. In addition, if anything, targeting gifts should
increase the gifts of altruists. Positive gift
externalities lead altruists to the free riding
problem, which implies that decreasing group
size will increase average contributions. However, it is not clear that altruists would perceive targeting gifts as reducing group size.
That is, if the group is defined as all recipients,
then the gifts of homogeneous altruists would
not be affected when gifts are targeted. On the
other hand, if the group is defined as those to
whom the altruist can personally give, then the
altruist would give more when gifts are targeted. However, in the experiment presented
in this article, we observe just the opposite:
players give less when gifts are targeted. Furthermore, other experimental studies have
found that the pure group size effect works
in the opposite direction than is predicted
by the free rider problem. For example, Isaac
and Walker (1988) and Isaac, Walker, and
Williams (1994) conducted a series of public
goods experiments to test for group size
effects. In their experiments, players divided
tokens between an individual investment
and a public investment. Returns from the
public investment were greater than those
from the private investment but were equally
divided among all players. While free riding
did occur, they found that increasing group
size actually decreased the free rider problem.
The experiments of Isaac and Walker
(1988) and Isaac, Walker, and Williams
(1994) were inspired by the public goods free
rider problem. As such, their experiments
are analogous to comparing a family with
10 cousins to a family with 20 cousins. The
experiments present in this article, on the other
hand, are analogous to comparing a family
that participates in a secret Santa gift exchange
with one that does not. That is, the unique feature of a secret Santa gift exchange is that it
does not reduce group size. Similarly, all the
treatments in the experiment described in this
article had 12 players. The treatments differed
only in how passed tokens were allocated to
recipients. What happens to giving in a secret
Santa gift exchange as the size of the group
increases is a question left for further research.
The free rider problem is a consequence of
a positive externality. The fact that players
contribute more when their recipients also
receive contributions from other players is
inconsistent with the free rider problem. If
the simplest explanation for why cooperation
would increase giving is that gifts carry a positive externality, then the simplest explanation
for why cooperation would decrease giving is
that gifts carry a negative externality. While
the traditional models of generosity imply that
giving carries either no externalities or only
positive externalities, in the sections that follow, I show that reasonable philanthropic
motives, such as impact philanthropy and
social comparison, do lead to negative gift
externalities. Furthermore, these models provide the simplest explanation for why targeting gifts would reduce giving.
B. Impact Philanthropy
One interpretation of the warm glow utility
function is to say that a philanthropist values
the act of giving because it makes him or her
feel like a good or generous person. Under this
interpretation, gi represents a gift given, and
thus, it makes no difference to the philanthropist what is actually done with his or her
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
contribution: its value is derived from giving it.
On the other hand, a gift given is also a gift
received. Another interpretation of the warm
glow utility function is to say that a philanthropist values personally helping a charitable
cause. Under this interpretation, gi represents
an increase in the charity’s budget. However,
if the true spirit of warm glow is that a philanthropist values personally helping a charity,
then simply entering gi into the philanthropist’s
utility function may not appropriately capture
this spirit. A philanthropist who cares about
personally helping a charitable cause should
not care about how his or her gift affects the
charity’s budget per se, but rather about how
it affects the production of charity. Duncan’s
(2004) impact philanthropy model shows that
this distinction is significant whenever the production of charity is strictly concave.
To understand the implications of impact
philanthropy, consider a philanthropist,
endowed with wealth wi, who receives utility
from personally increasing the supply of m
charitable goods. Expanding on the earlier
notation, let gij represent philanthropist i’s
contribution to the production of charitable
good j. Let Z(Gj) represent the production
technologies of the charitable goods, where
Z# . 0 and Z0 , 0. Thus, for the impact philanthropy model to be applied to an experimental game, a player’s utility derived from
playing the game must be concave in payoffs.
In all models of generosity, a philanthropist
would prefer to target his or her contribution
at his or her favorite charitable good. The
impact philanthropy model is unique because
it predicts that an impact philanthropist would
prefer to target his or her contribution even
when the charitable goods are perfect substitutes. For example, define the aggregate production of charity as:
ð1Þ
W5
m
X
ZðGj Þ:
j51
By definition, an altruist values the level of
W, aP
warm glow philanthropist values increasing j Gj , and an impact philanthropist values
increasing W. The amount that i increases W,
his or her impact, is calculated as:
ð2Þ
di 5
X
j
ðZðGj Þ ZðGij ÞÞ;
13
where Gij 5 Gj gij represents the total gift
given to good j from all donors except i.
Thus, a pure impact philanthropist’s utility
function is written as:
X
ð3Þ
gij Þ þ fi ðdi Þ;
vi 5 Ui ðwi j
where Ui and fi are increasing, strictly concave
functions.20
An impact philanthropist is someone who
enjoys impacting the supply of charity. The
calculation of impact assumes that each philanthropist views him or herself as giving the
last dollar.21 Unfortunately for the impact
philanthropists, the last dollar given has the
least impact. As a result, impact philanthropy
can lead donors to a kind of codependent
behavior, because it suggests that donors
can benefit from need. Specifically, Equation
(3) implies that
ð4Þ
@vi
, 0; whenever gij . 0:
@Gij
The contributions of other donors can
make an impact philanthropist worse off, ceteris paribus, because it reduces the influence of
his or her contribution.22 As in the altruist
model, gift interdependency in the impact philanthropy model provides donors an incentive
to cooperate with each other. However, unlike
altruists, cooperation among impact philanthropists can decrease giving because in its
20. The additive utility functions are for illustrative
purposes only. All the conclusions derived in this article
generalize to the case of general preferences.
21. This calculation of impact holds constant the gifts
of other donors. However, it is not required that a philanthropist, say sponsoring a child, be so naive that he or she
believes that, but for his or her contribution, others would
let the child starve. It only requires that gratitude follow
the donation. A sponsored child is not likely to say,
‘‘thanks, but we both know that if you had not saved
me, someone else would have.’’ In this respect, impact philanthropy is similar to warm glow—it is the feeling a donor
gets from personally increasing the supply of a charitable
good.
22. Impact philanthropy, because it implies negative
gift externalities, leads to some seemingly unphilanthropic
behavior. To identify, understand, and test for this behavior, this section discusses a model of pure impact philanthropy in which a philanthropist enjoys impacting the
supply of a good without also enjoying its actual supply.
In the end, it would be reasonable to assume that a philanthropist enjoys the size, impact, and end result of his or
her gift.
14
ECONOMIC INQUIRY
X
absence, philanthropists fail to account for
a negative gift externality.
ð7Þ U # ðw C. Targeting Gifts at Specific Recipients
Let g~ 5 f~
gij g "ij be the equilibrium gift
allocation that solves Equation (7). It is
j "j,
~j , G
straightforward to prove that G
meaning that total giving is less when gifts
are targeted at individual recipients. Suppose
not. If i were to give the same amount, or
more, when gifts are targeted, then
X
X
ð8Þ U # ðw g~ij Þ U # ðw gij Þ; "j 2 Ji ;
The experiment was designed to test how
targeting gifts, as opposed to spreading them
around, will affect giving. For an altruist, any
gij g such
two
f
gij g and
P
P f~
P that
P gift allocations
~
~ij "j
5
"i
and
5
g
g
g
ij
ij
ij
j
j
i
ig
are equivalent. That is, reallocating gifts such
that each philanthropist gives the same total
gift, and each charitable good receives the
same total gift, will not affect an altruist’s utility. The same is true for a warm glow philanthropist. Conversely, reallocating gifts, even
while holding W constant, can increase an
impact philanthropist’s utility. For impact
philanthropists, targeting gifts is a form of
cooperation. By entering into an agreement
in which each donor only gives to specific
recipients, an impact philanthropist can enjoy
giving the first, as well as the last, dollar to
a recipient. The simplest example of such an
agreement is one with n homogeneous donors,
m goods, and in which n 5 km, where k is
a positive integer. In this situation, a targeted-gift agreement in which each donor’s
contribution is targeted at k goods, such
that no two donors give to the same good, will
decrease aggregate giving. To see why, let g 5
f
gij g "ij be the symmetric Nash equilibrium
gift allocation when each donor’s contribution
is divided equally among the m goods. The
first-order condition for an interior solution
to choosing gifts that maximize Equation (3)
among homogeneous donors is
X
ð5Þ
gij Þ 5 f # ðdi ÞZ # ðGj Þ;
U # ðw j
for j 5 1; . . . ; m;
P
where di 5
j ðZðGj Þ ZðGij ÞÞ. Let Ji represent the set of k goods that i may contribute
to when contributions are targeted. Gifts are targeted such that Jk \ Jl is an empty set "k 6¼ l.
When donor i can contribute only to goods in
Ji, his or her utility is
X
vi 5 U ðw ð6Þ
gij Þ þ f ðdi Þ;
j
P
where di 5
j2Ji ðZðGj Þ Zð0ÞÞ. The firstorder condition for an interior solution to
choosing gifts that maximize Equation (6) is
gij Þ 5 f # ðdi ÞZ # ðGj Þ; "j 2 Ji :
j
j
j
ð9Þ
~ j Þ Z # ðG
j Þ; "j 2 Ji ;
Z # ðG
ð10Þ
~di . di :
Equation (10) is the result of the strict concavity of Z. Given Equations (8) and (9), to
satisfy Equation (7), it must be true that
ð11Þ
f # ð~di Þ f # ðdi Þ; "j 2 Ji :
Equations (10) and (11) contradict the
strict concavity of f. Therefore, total giving
must go down when gifts are targeted at
specific recipients.23
In the experimental design presented above,
k is a positive integer. However, in real-world
examples, there may or may not be an evenly
divisible donor-to-recipient ratio. Even if k is
not an integer, it would still be feasible to
arrange several targeted-gift agreements. For
example, if k . 1, but is not an integer, then
one possible targeted-gift agreement would
have donors target their gifts at as many goods
as possible (i.e., the integer part of n/m) while
allowing every donor to also contribute to the
remainder goods. Equilibrium would require
that each good be given the same gift; otherwise the marginal impact of giving to one’s targeted goods would be greater than (or less
23. It is natural to ask, ‘‘If targeted gifts lower total
giving, then why would a charitable organization offer this
option?’’ Charitable organizations may offer target giving
for the same reason that for-profit firms compete, even
though competition lowers an industry’s total profit. Different charitable organizations compete for the same charitable dollar. Just as competition forces for-profit firms
into lowering price and increasing supply, it may also force
nonprofit firms into offering targeted giving.
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
than) giving to the remainder goods. On the
other hand, if k , 1, and n and m share the
common factor u, then an example of a targeted-giving agreement would have groups
of n/u donors give exclusively to groups of
m/u goods.
All the targeted-gift agreements discussed
previously have one thing in common: they
are symmetric. A symmetric targeted-gift
agreement is one in which if every donor were
to give the same gift, then every donor would
calculate the same impact. For example, allocating more goods to one donor than to
another would not be symmetric. It also means
that if every donor were to give the same
amount, then every good would receive the
same amount—that is, leaving some recipients
out is not symmetric. Depending on the donorto-recipient ratio, it may or may not be feasible
to arrange a symmetric targeted-gift agreement. However, using the same proof by contradiction logic as above, any symmetric
sponsoring agreement among homogeneous
donors, if feasible, will result in smaller gifts
regardless of the donor-to-recipient ratio.
The previous discussion applies to situations with homogeneous donors. If donors
are heterogeneous, then a targeted-giving
agreement can either increase or decrease giving. For example, consider a family with 20
homogeneous cousins, each of whom spends
$95 a year buying Christmas presents for his
or her fellow cousins. As a result, each cousin
receives nineteen $5 gifts. This year, however,
the cousins agree to a secret Santa gift
exchange in which each cousin will buy a gift
for one other cousin. How will total holiday
spending this year compare with years past?
The secret Santa gift exchange lowers the price
of impact (d). As a result, each cousin will buy
more impact. However, he or she will end up
spending less money (gi). That is, the impact
philanthropy model predicts that each cousin
will spend less than $95 on his or her gift while
at the same time feel that he or she has a greater
impact (i.e., gave a more meaningful gift) than
in years past. However, suppose instead that
the cousins are heterogeneous. Specifically,
suppose that one rich cousin plans to buy each
of his or her fellow cousins a $50 gift. The rich
cousin may not be willing to enter into a secret
Santa gift exchange, but if forced to, the allocation of presents among the cousins will
become unequal, with one lucky recipient.
For the rich cousin, the cost of increasing the
15
utility of his or her fellow cousins goes up, while
for the poorer cousins, it goes down. Thus, targeting gifts can have an ambiguous effect on
giving when donors are heterogeneous.
D. Social Comparison and Prestige
Impact philanthropy begins with a
straightforward assumption: donors want
their contributions to make a difference.
The negative gift externalities implied by this
assumption distinguishes impact philanthropy from conventional models of philanthropy. However, the calculation of impact
given by Equation (2) is just one in a class
of utility specifications that produce negative
gift externalities. Others include social comparison and prestige, such as a donor who
cares about how his or her gift measures up
to the gifts of others (Harbaugh 1998).24
While these, too, are straightforward assumptions, they can also lead to negative gift
externalities. For example, consider a rank
philanthropist’s utility function written as
ð12Þ
vi 5 ui ðxi ; rankðgi ÞÞ:
Giving by others will hurt a rank philanthropist if it increases the cost of achieving
ones desired rank. It is not clear if a rank philanthropist would want to calculate his or her
rank among the recipients of his or her gift or
among other donors. Presumably, this would
depend on who a rank philanthropist wants to
impress: recipients or fellow donors. The latter
implies no difference between targeting gifts
and spreading them around, because different
ways of allocating gifts would not change
a donor’s overall rank. However, the former
implies that targeting gifts will reduce giving.
For example, when a donor sponsors a child,
does he or she calculate a rank of 1? This might
not be unreasonable, given that no one else is
giving to that child and that the child’s gratitude might follow the dollar. If so, then, just as
in the impact philanthropy model, targeting
gifts removes a negative externality, and so
donors will contribute less.
24. In Harbaugh’s (1998) model, prestige is an absolute concept derived from publicly announcing a philanthropist’s gift. Social comparison models extend
prestige to a relative concept derived from how large a philanthropist’s gift is compared to other gifts.
16
ECONOMIC INQUIRY
A more general type of rank philanthropist
is one who wants his or her gift to hit a relative
target. Consider the utility
ð13Þ
vi 5 Ui ðxi ; bi ðgi X
hij gj Þ2 Þ;
j6¼i
where bi and hij represent utility weights.25 An
increase
P in the giving by others moves the target, j6¼i hij gj , making i worse-off. Again, if
the target is a function of all gifts, then targeting gifts will not affect giving. However, if
a donor’s target is only a function of the gifts
given to the good he or she contributes to, then
targeting removes a negative gift externality
and can reduce giving.
VI. DISCUSSION
At the end of the experiment, players were
asked how they decided how many tokens to
pass. Of course, none of the participants mentioned altruism, philanthropy, or even generosity, but many spoke of what they thought
seemed ‘‘fair.’’ For example, participants were
asked what they thought about the idea of
passing 50 of their 100 tokens. There was
a recurring theme in the answer to this question. Participants in the one-recipient treatment groups routinely said that 50 tokens
was too much because, to paraphrase, ‘‘if I
were to pass 50 tokens, then I would get 50
points from my tokens while someone else
would get 100 points from my tokens. This
doesn’t seem fair.’’ Participants in the fiverecipient treatment group, however, routinely
said that passing 50 tokens seemed fair, even if
they personally chose to pass less. When confronted with the logic that arose in the onerecipient treatment groups, participants in
the five-recipient treatment groups routinely
said that, paraphrasing again, ‘‘if I were to
pass 50 tokens, then I would get 50 points
from my tokens while 5 other players would
get 20 points from my tokens. I get 50, they
get 20, this seems fair.’’
The anecdotal perception of fairness
expressed by participants is different from
25. This utility function appeared in the working
paper version of Andreoni and Petrie (2004) but was
removed prior to publication.
the concept of fairness discussed by experimental economists. For example, Rabin
(1993) develops a model of kindness in which
people reward those who are kind to them and
punish those who are unkind. This concept of
fairness seems to be born out in the ultimatum
game, in which players routinely punish other
players who they deem as playing unfair
(Güth, Schmittberger, and Schwarze 1982;
Roth and Erve 1995). Conversely, when the
players in this experiment were using the word
‘‘fair,’’ they were using it to describe their gift’s
impact or perceived generosity. When a gift
was given to one recipient, players perceived
a large impact, but when the same gift was
divided among five recipients, players perceived a smaller impact. Thus, it is not clear
whether the players’ description of fairness
is conceptually different from impact philanthropy or social comparison. Regardless, if
increasing one player’s gift requires another
player to increase his or her gift out of ‘‘fairness,’’ then fairness also implies a negative gift
externality.
The experiment reported in this study was
designed to determine what effect, if any, targeting an individual’s gift at a smaller group of
recipients has on giving. In a modified version
of the dictator game, I find that participants
give less when their gifts are targeted. Conventional models of generosity, such as altruism
and warm glow, cannot explain this result.
Therefore, while there is little doubt that the
conventional models of generosity capture
important motives for giving, the experimental findings of this and other studies suggest
that donors must have some additional
motives to give. Furthermore, the experimental results of this study offer unique insights
into the characteristics of these additional
motivations. For instance, rather than reducing their contributions and free riding off of
the gifts of others, players increase their contributions when others are allowed to give to
their recipients. This result suggests that gifts
carry a negative externality. While conventional models of generosity suggest only positive externalities, this article shows that
reasonable philanthropic assumptions, such
as impact philanthropy and social comparison, can lead to negative gift externalities.
In these models, giving by others creates a negative externality because it reduces the importance, perceived generosity, or social status of
one’s gift.
DUNCAN: SECRET SANTA REVEALS SECRET SIDE
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