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Secret Santa reveals the secret side of giving.

I. INTRODUCTION

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 persona 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 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 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 average 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 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 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 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)

[FIGURE 1 OMITTED]

This experiment deviates from the typical dictator game in several important ways. 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 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)

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 five-recipient 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 men (13) 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 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.

[FIGURE 2 OMITTED]

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 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, Gachter, and Fehr 2001). Although strategic 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.

[FIGURE 3 OMITTED]

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 notable 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 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 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, [g.sub.it] = f([r.sub.it-1]). 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 [r.sub.1t] and [r.sub.2t]. 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 [bar.r] and give [??] in the following round. Total giving by Players 3 and 4 in the following round is 2[??]. In the second session, when gifts are targeted, Player 3 receives [r.sub.1t-1] and gives [g.sub.3t] in the following round, while Player 4 receives [r.sub.2t-1] and gives [g.sub.4t] in the following round. Total giving by Players 3 and 4 in the following round is 2[bar.g], which is less than 2[??] 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 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 five-recipient treatment knew that he of 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.

[FIGURE 4 OMITTED]

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, 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, [x.sub.i], but also has the opportunity to make a charitable contribution, [g.sub.i]. 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, nonexcludable public good G, where G = [[SIGMA].sub.i][g.sub.i]. The altruist's utility function, written [u.sub.i]([x.sub.i], 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 [u.sub.i]([x.sub.i],[g.sub.i]), 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 of her feel like a good of generous person. Under this interpretation, [g.sub.i] represents a gift given, and thus, it makes no difference to the philanthropist what is actually done with his or her 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, [g.sub.i] 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 [g.sub.i] 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 [w.sub.i], who receives utility from personally increasing the supply of m charitable goods. Expanding on the earlier notation, let [g.sub.ij] represent philanthropist i's contribution to the production of charitable good j. Let Z([G.sub.j]) represent the production technologies of the charitable goods, where Z' > 0 and Z" < 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:

(1) [PSI] = [m.summation over (j = 1)] Z([G.sub.j]).

By definition, an altruist values the level of [PHI], a warm glow philanthropist values increasing [[SIGMA].sub.j] [G.sub.j], and an impact philanthropist values increasing [PSI]. The amount that i increases [PSI], his or her impact, is calculated as:

(2) [[delta].sub.i] = [summation over (j)] (Z([G.sub.j]) - Z([G.sub.-ij])),

where [G.sub.-ij] = [G.sub.j] - [g.sub.ij] represents the total gift given to good j from all donors except i.

Thus, a pure impact philanthropist's utility function is written as:

(3) vi = [U.sub.i]([w.sub.i] - [summation over (j)] [g.sub.ij]) + [f.sub.i]([[delta].sub.i]),

where [U.sub.i] and [f.sub.i] 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

(4) [partial derivative][v.sub.i]/[partial derivative][G.sub.-ij] < 0, whenever [g.sub.ij] > 0.

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 absence, philanthropists fail to account for a negative gift externality.

C. Targeting Gifts at Specific Recipients

The experiment was designed to test how targeting gifts, as opposed to spreading them around, will affect giving. For an altruist, any two gift allocations {[[bar.g].sub.ij]} and {[[??].sub.ij]} such that [[SIGMA].sub.j] [[bar.g].sub.ij] = [[SIGMA].sub.j] [[??].sub.ij] [for all]i and [[SIGMA].sub.i] [[bar.g].sub.ij] = [[SIGMA].sub.i] [[??].sub.ij] [for all]j 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 [PSI] 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 = [lambda]m, where [lambda] is a positive integer. In this situation, a targeted-gift agreement in which each donor's contribution is targeted at [lambda] goods, such that no two donors give to the same good, will decrease aggregate giving. To see why, let [bar.g] = {[[bar.g].sub.ij]} [for all]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

(5) U' (w - [summation over (j)] [g.sub.ij]) = f' ([[delta].sub.i])Z'([G.sub.j]), for j = 1,..., m,

where [[delta].sub.i] = [[SIGMA].sub.j](Z([G.sub.j]) - Z([G.sub.-ij])). Let [J.sub.i] represent the set of [lambda] goods that i may contribute to when contributions are targeted. Gifts are targeted such that [J.sub.k] [intersection] [J.sub.l] is an empty set [for all]k [not equal to] l. When donor i can contribute only to goods in [J.sub.i], his of her utility is

(6) [v.sub.i] = U(w - [[summation over (j)] [g.sub.ij]) + f([[delta].sub.i]),

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The first-order condition for an interior solution to choosing gifts that maximize Equation (6) is

(7) U' (w - [summation over (j)] [g.sub.ij]) = f' ([[delta].sub.i])Z'([G.sub.j]), [for all]j [member of] [J.sub.i].

Let [??] = {[[??].sub.ij]} be the equilibrium gift allocation that solves Equation (7). It is straightforward to prove that [G.sub.j] < [G.sub.j] [[for all].sub.j], 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

(8) U' (w - [summation over (j)] [[??].sub.ij]) [greater than or equal to] U' (w - [summation over (j)][[bar.g].sub.ij]), [for all]j [member of] [J.sub.i],

(9) Z'([??].sub.j]), [less than or equal to] Z' [[bar.G].sub.j], [for all]j [member of] [J.sub.i],

(10) [[??].sub.i] > [[bar.[delta].sub.i].

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

(11) f'([[??].sub.i]) [greater than or equal to] f'([[bar.[delta].sub.i]), [for all]j [member of] [J.sub.i].

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, [lambda] is a positive integer. However, in real-world examples, there mayor may not be an evenly divisible donor-to-recipient ratio. Even if [lambda] is not an integer, it would still be feasible to arrange several targeted-gift agreements. For example, if [lambda] > 1, but is not ah 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 than) giving to the remainder goods. On the other hand, if [lambda] < 1, and n and m share the common factor [phi], then an example of a targeted-giving agreement would have groups of n/[phi] donors give exclusively to groups of m/[phi] 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 donor-to-recipient ratio, it may of 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 of 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 ([delta]). As a result, each cousin will buy more impact. However, he or she will end up spending less money ([g.sub.i]). That is, the impact philanthropy model predicts that each cousin will spend less than $95 on his of her gift while at the same time feel that he of 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 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

(12) [v.sub.i] = [u.sub.i]([x.sub.i], rank([g.sub.i])).

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 of 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.

A more general type of rank philanthropist is one who wants his or her gift to hit a relative target. Consider the utility

(13) [v.sub.i] = [U.sub.i]([x.sub.i], [[beta].sub.i][([g.sub.i] - [summation over (j [not equal to] i)] [[theta].sub.ij][g.sub.j]).sup.2]),

where [[beta].sub.i] and [[theta].sub.ij] represent utility weights. (25) An increase in the giving by others moves the target, [[SIGMA].sub.j[not equal to]i] [[theta].sub.ij][g.sub.j], 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 five-recipient 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 one-recipient 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 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 (Guth, 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.

ABBREVIATION

OLS: Ordinary Least Squares

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Duncan, B. "A Model of Impact Philanthropy." Journal of Public Economics, 88, 2004, 2159-80.

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Eckel, C., and P. Grossman. "Differences in the Economic Decisions of Men and Women: Experimental Evidence," in Handbook of Results in Experimental Economics, edited by C. Plott and V. Smith, Amsterdam: North Holland/Elsevier Press: 2006.

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Guth, W., R. Schmittberger, and B. Schwarze. "An Experimental Analysis of Ultimatum Bargaining." Journal of Economic Behavior and Organization, 3, 1982, 367-88.

Harbaugh, W. "What Do Donations Buy? A Model of Philanthropy Based on Prestige and Warm Glow." Journal of Public Economics, 67, 1998, 269-84.

Isaac, R. M., and J. M.. Walker. "Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism." Quarterly Journal of Economics, 103, 1988, 179-99.

Isaac, R. M., J. M. Walker, and A. W. Williams. "Group Size and the Voluntary Provision of Public Goods: Experimental Evidence Utilizing Large Groups." Journal of Public Economics, 54, 1994, 1-36.

Menchik, P., and B. Weisbrod. "Volunteer Labor Supply in the Provision of Collective Goods," in Non-Profit Firms in a Three Sector Economy, edited by M. White. Washington, DC: The Urban Institute, 1981, 163-81.

Rabin, M. "Incorporating Fairness into Game Theory and Economics." American Economic Review, 1993, 83, 1281-1302.

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Stiglitz, J. "Pareto Efficient and Optimal Taxation and the New Welfare Economics," in Handbook of Public Economics, Vol. II, edited by A. J. Auerbach and M. Feldstein. Amsterdam, The Netherlands: North Holland, 1987, 991-1042.

Warr, P. "Pareto Optimal Redistribution and Private Charity." Journal of Public Economics, 19, 1982, 131-38.

Brian Duncan, 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 brian.duncan@cudenver.edu

doi: 10.1111/j.1465-7295.2008.00145.x

Online Early publication May 18, 2008

(1.) In fact, organizers often ensure this result by placing a limit on the amount of money each participant may spend on a gift.

(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 hall 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.

(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.

(5.) The instruction sheet and rules of the game can be ownloaded at http://www.econ.cudenver.edu/bduncan.

(6.) There were three sessions each of the one- and five-recipient 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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(25.) This utility function appeared in the working paper version of Andreoni and Petrie (2004) but was removed prior to publication.
TABLE 1 Percent of Endowment Contributed to Recipients per Round

 All Participants

 Recipients

 One Three Five
Round
 1 30.36 (4.72) 43.71 (6.77) 44.83 (5.61)
 2 29.69 (4.81) 46.46 (7.62) 46.94 (5.25)
 3 29.89 (5.77) 41.83 (7.09) 47.83 (6.11)
 4 27.94 (5.94) 36.63 (7.53) 41.57 (5.51)
 5 21.17 (4.84) 33.50 (6.31) 40.20 (5.34)
 6 18.08 (4.63) 34.79 (6.52) 40.47 (6.21)
 7 18.00 (4.77) 31.88 (7.56) 32.83 (6.06)
 8 16.03 (4.75) 25.04 (7.34) 31.04 (5.70)
Last round
 Difference 9.01 (8.35) 6.00 (9.2)
 Sum(a) 15.01** (7.42)
All rounds 23.90 (1.80) 36.73 (2.51) 40.72 (2.03)
 Difference 12.83*** (3.01) 3.99 (3.22)
 Sum(a) 16.82*** (2.71)

 Male Participants

 Recipients

 One Three Five
Round
 1 36.53 (7.16) 46.6 (9.19) 46.75 (9.46)
 2 36.68 (7.11) 53.33 (10.32) 54.13 (8.49)
 3 35.63 (8.31) 44.6 (9.34) 54.68 (8.45)
 4 38.47 (9.21) 37.6 (9.80) 48.67 (8.98)
 5 28.79 (7.90) 35.27 (8.19) 52.14 (8.36)
 6 24.47 (7.67) 40.33 (8.23) 48.44 (10.37)
 7 24.74 (7.02) 33.00 (10.44) 41.13 (10.61)
 8 13.79 (6.08) 22.67 (9.49) 34.84 (9.31)
Last round
 Difference 8.8 (10.85) 12.18 (13.29)
 Sum(a) 21.05*(10.80)
All rounds 29.89 (2.71) 39.18 (3.33) 47.6 (3.24)
 Difference 9.29** (4.24) 8.42* (4.64)
 Sum(a) 17.71*** (4.19)

 Female Participants

 Recipients

 One Three Five
Round
 1 23.47 (5.74) 38.89 (10.03) 43.30 (6.90)
 2 21.88 (6.04) 35.00 (10.37) 41.20 (6.47)
 3 23.47 (7.9) 37.22 (11.28) 42.35 (8.68)
 4 16.18 (6.35) 35.00 (12.42) 35.90 (6.78)
 5 12.65 (4.62) 30.56 (10.39) 30.65 (6.28)
 6 10.94 (4.37) 25.56 (10.56) 34.10 (7.43)
 7 10.47 (6.05) 30.00 (10.93) 26.20 (6.74)
 8 18.53 (7.57) 29.00 (12.15) 28.00 (7.21)
Last round
 Difference 10.47 (13.63) -1.00 (13.46)
 Sum(a) 9.47 (10.48)
All rounds 17.20 (2.18) 32.65 (3.74) 35.21 (2.50)
 Difference 15.45*** (4.04) 2.56 (4.50)
 Sum(a) 18.01*** (3.37)

Notes: Of the 96 participants, 50 were male and 46 were female.
Standard errors are given in parentheses.

(a) The sum equals the difference between the one- and
five-recipient sessions.

Statistically significant at the ***99%, **95%,
and *90% confidence levels.

TABLE 2 Percent of Contributions Equal to 0% or 100% of the Player's
Endowment

 Contributed 0%

 Recipients

 One Three Five
Round 1 19.4 (6.7) 12.5 (6.9) 8.3 (4.7)
 Difference -6.9 (9.9) -4.2(8.0)
 Sum(a) -11.1 (8.2)
Round 8 61.1 (8.2) 54.2 (10.4) 25.0 (7.3)
 Difference -6.9* (13.2) -29.2*(12.3)
 Sum(a) -36.1***(11.0)
All rounds 38.50 (2.9) 26.6 (3.2) 14.9 (2.1)
 Difference -12.0*** (4.4) -11.6*** (3.7)
 Sum(a) -23.6*** (3.6)

 Contributed 100%

 Recipients

 One Three Five
Round 1 2.8 (2.8) 16.7 (7.8) 16.7 (6.3)
 Difference 13.9* (7.2) 0.0 (10.0)
 Sum(a) 13.9** (6.9)
Round 8 5.6 (3.9) 12.5 (6.9) 11.1 (5.3)
 Difference 6.9 (7.4) -1.4(8.6)
 Sum(a) 5.6 (6.6)
All rounds 3.10 (1.0) 12.5 (2.4) 14.6 (2.1)
 Difference 9.4*** (2.3) 2.1 (3.2)
 Sum(a) 11.5*** (2.3)

Note: Standard errors are given in parentheses.

(a) The sum equals the difference between the one- and
five-recipient sessions. Statistically significant at the
***99%, **95%, and *90% confidence levels.

TABLE 3
Marginal Effects Calculated from Two-Way Censored
Tobit Regressions

 (1) (2)
Treatment
 Three recipients 13.87 *** (3.20) 10.19 *** (3.51)
 Five recipients 19.26 *** (2.76) 22.18 *** (3.20)
Round
 2 0.04 (4.60) 0.01 (4.54)
 3 1.03 (4.59) -1.17 (4.53)
 4 -5.84 (4.40) -6.04 (4.33)
 5 -8.01 * (4.29) -8.29 * (4.22)
 6 -9.22 ** (4.25) -9.31 ** (4.19)
 7 13.03 *** (4.06) -13.42 *** (3.99)
 8 -17.13 *** (3.83) -17.30 *** (3.77)
Age (yr)
 26-35 0.53 (3.49)
 36 or older 3.06 (6.42)
Friends 1.51 ** (0.58)
Female 10.97 *** (2.35)
Ethnicity
 Black -11.67 *** (4.10)
 Asian -11.60 *** (3.58)
 Other -10.55 *** (3.14)
Foreign born -0.48 (3.17)
Employed 3.74 (2.58)
Received
 Lag
 [Lag.sup.2]/1,000
 Sum
 [Sum.sup.2]/1,000
 Average
 [Average.sup.2]
 / 1,000
Likelihood ratio 77.86 122.35
Sample size 768 768

 (3) (4)
Treatment
 Three recipients 11.15 *** (4.28) 8.20 ** (4.00)
 Five recipients 24.04 *** (4.23) 20.23 *** (3.94)
Round
 2
 3 -1.41 (4.51) -2.55 (4.74)
 4 -6.52 (4.30) -8.52 * (4.93)
 5 8.33 ** (4.20) 11.69 ** (5.15)
 6 -8.95 ** (4.19) -13.56 ** (5.28)
 7 13.15 *** (3.97) 18.15 *** (5.03)
 8 -17.04 ** (3.77) -22.31 *** (4.68)
Age (yr)
 26-35 -1.70 (3.71) -0.93 (3.79)
 36 or older 3.81 (6.89) 3.63 (6.87)
Friends 1.69 *** (0.63) 1.69 *** (0.62)
Female 11.29 *** (2.51) -11.57 *** (2.52)
Ethnicity
 Black -10.94 ** (4.41) -10.86 ** (4.42)
 Asian -11.85 *** (3.80) -11.82 *** (3.80)
 Other -9.69 *** (3.37) -9.40 *** (3.41)
Foreign born -0.43 (3.39) -0.15 (3.41)
Employed 3.74 (2.77) 3.68 (2.77)
Received
 Lag -0.07 (0.09)
 [Lag.sup.2]/1,000 0.58 (0.53)
 Sum 0.02 (0.03)
 [Sum.sup.2]/1,000 0.001 (0.033)
 Average
 [Average.sup.2]
 / 1,000
Likelihood ratio 111.95 111.92
Sample size 672 672

 (5)

Treatment 8.28 ** (4.06)
 Three recipients 20.28 *** (4.02)
 Five recipients
Round
 2 -1.15 (4.52)
 3 -5.82 (4.33)
 4 -7.75 * (4.26)
 5 -8.56 ** (4.24)
 6 12.50 *** (4.04)
 7 -16.27 *** (3.81)
 8
Age (yr) -0.53 (3.81)
 26-35 3.44 (6.86)
 36 or older 1.71 *** (0.63)
Friends -11.64 *** (2.52)
Female
Ethnicity -10.71 ** (4.43)
 Black -11.60 *** (3.80)
 Asian -9.38 *** (3.41)
 Other 0.16 (3.40)
Foreign born 3.63 (2.77)
Employed
Received
 Lag
 [Lag.sup.2]/1,000
 Sum
 [Sum.sup.2]/1,000 0.03 (0.14)
 Average 0.31 (0.81)
 [Average.sup.2]
 / 1,000 113.49
Likelihood ratio 672
Sample size

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.
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Author:Duncan, Brian
Publication:Economic Inquiry
Geographic Code:1USA
Date:Jan 1, 2009
Words:11080
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