Children's Altruism in Public Good and Dictator

CHILDREN’S ALTRUISM IN PUBLIC GOOD AND DICTATOR EXPERIMENTS WILLIAM T. HARBAUGH and KATE KRAUSE*

We examine the de¨elopment of altruistic and free-riding beha¨ior in 6᎐12-year-old children. We find that the le¨el of altruistic beha¨ior in children is similar to that of adults but that repetition has a different effect. Younger children’s contributions tend to increase in later rounds of the experiments, whereas the contributions of older children, like those of adults, tend to decline. Group attachment is associated with higher contributions. Contributions in a subsequent dictator experiment are corre- lated with first-round contributions in the public good experiment, but are not strongly correlated with last-round contributions.Ž. JEL H41

I. INTRODUCTION way similar to adults, the taste for altruism Research on altruism among adults using must be, if not innate, at least determined by linear public good experiments has estab- very early experiences. Next, since hetero- lished a number of interesting results. Adults geneity in altruistic behavior may be due to are initially far more generous than would be differences in these experiences, we test true if they were motivated by plain selfish- whether the variance in children’s altruistic ness. With repetition, most gradually start to behavior is correlated with demographic and free-ride, but many continue to contribute other variables. The observed decline in con- substantial amounts, suggesting that a taste tribution among adults suggests that at least for altruism is, if not universal, at least some adults learn the free-riding strategy widespread. The existence of such a prefer- over the course of the experiment or that ence is confirmed by a wide variety of behav- confusion regarding the protocol is reduced iors in nonexperimental settings. Since altru- with repeated play. There is evidence that istic behavior is an important feature of the adults are confused by the experimental pro- economy, a natural, and important, question tocol, and it is plausible that children might is to ask were it comes from. As a first step be even more so. To determine whether toward addressing this question, in this arti- learning about either the free-riding strategy cle we examine the behavior of 6- to 12-year- or about the protocol is age-related, we in- old children in public good experiments. vestigate how behavior in this experiment We begin by comparing the extent of al- differs across children of different ages. Fi- truistic behavior in children with that of adults. If even young children behave in a nally, to test whether the linear public goods game is a reasonable way of studying altru- ism in children, we conduct a second test of *This research was funded by grants from the Uni- altruism, based on the dictator game, on a versity of New Mexico Research Allocation Committee and the National Science Foundation. We thank Jim subset of the original subjects. Andreoni, Arik Levinson, Lise Vesterlund, Jim Ziliak, In a typical linear public goods experi- and an anonymous referee for helpful comments. We ment subjects are recruited and put into would also like to express our appreciation to the City of Albuquerque recreation program leaders for their groups of N members, where N is generally help organizing and conducting these experiments, and between 4 and 10. Subjects play either a to give our thanks to the children who participated. preannounced or randomly determined num- Harbaugh: Assistant Professor, Department of Eco- ber of rounds. At the beginning of each nomics, University of Oregon, Eugene, Oregon 97403-1285, Phone 541-346-1244, Fax 541-346-1243, round, subjects are endowed with experi- E-Mail [email protected] ment currency that is exchanged for cash at Krause: Assistant Professor, Department of Economics, the end of the experiment. They then must 1915 Roma NE, University of New Mexico, Albu- querque, New Mexico 87131-1101, Phone 505-277- decide whether to keep it or to contribute 3429, Fax 505-277-9445, E-Mail [email protected] any portion of it to the group. The money

95 Economic Inquiry Ž.ISSN 0095-2583 Vol. 38, No. 1, January 2000, 95᎐109 ᮊWestern Economic Association International 96 ECONOMIC INQUIRY given to the group is multiplied by a number tition. In contrast, the experiments we report ␣ greater than 1 but less than N, and then in this article were conducted in a controlled the total is divided equally among the group environment that provided for anonymity and members. In this game, the individually ra- real consequences, making them very similar tional strategyŽ. for selfish preferences is to to those that economists have conducted on donate nothing in each round, while the adults. Pareto optimal result is for each person to One problem with using the linear public donate everything. good experiment to estimate altruism is that, Ledyardwx 1995 provides more information for selfish players, the Nash equilibrium is to on these experiments and summarizes the give nothing, and negative donations are im- conclusions. The result is typically that peo- possible. This means that any mistakes will ple donate between one-third and two-thirds be counted as altruism. While the original of their endowments to the group, that they motivation for repeating the game was so donate more if ␣rN Žthe marginal private that subjects’ mistakes would be reduced by return. is larger, and that donations decrease learning, two recent articles have addressed with repetition, though not to zero. These the issue of confusion more directly. By pay- results are generally taken as proof that the ing subjects according to their relative earn- subjects have a taste for altruism. The over- ings, or rank, as opposed to their absolute whelming majority of these experiments have earnings, Andreoniwx 1995 alters the standard been conducted using college undergradu- public goods experiment so that confusion is ates, although one of the earliest studies, the only motive for contributing. Palfrey and Marwell and Ameswx 1981 used high school Prisbeywx 1998 include parameters for which students. the Nash equilibrium contribution is posi- We have been able to find only one exist- tive. Both find a substantial amount of con- ing study by economists that is concerned fusion, even after 10 repetitions, but also a with the altruistic behavior of children. This substantial amount of altruism. article, by Peters, Unur, Clark, and Schulze If children are more likely than adults to wx1997 , uses linear public good experiments make mistakes, or to be slower at learning, to test children’s altruism toward family then the public goods experiment will tend members, focusing on the rotten-kid theo- to overestimate children’s altruism relative rem. They find that in this setting children to that of adults. Although we felt that the give less than parents and that children’s protocols used by Andreoni and by Palfrey contributions generally do decline with repe- and Prisbey to compute measures of the tition. Developmental psychologists have effect of confusion would be very difficult to done a considerable amount of work on the implement with children, we did run a simple altruistic behavior of children. Eisenberg and test of the consistency of the behavior of our Mussenwx 1989 has a good review of this. subjects across two different protocols. At Underwood and Moorewx 1982 report that three sites, we followed the public good ex- age has generally been found to be positively periment by having children play a simple correlated with both frequency and levels of dictator game, modeled after Andreoni and contributions. They also note that gender Millerwx 1998 , that asked them to make do- has been found to be correlated with gen- naterkeep decisions under varying pricing erosity more often than not. Measures of conditions. We argue that, because the in- ‘‘prosocial’’ behaviors and advanced levels of centives are very clear, errors in the dictator ‘‘moral judgment’’ on the part of children game are likely to be small and that further- have also been associated with generosity. more there is no reason they should be bi- The methodology used in studies by develop- ased in either direction. So, behavior in these mental psychologists varies widely and is of- two games should be highly correlated, un- ten very different from that typically used in less it is diminished by confusion in the economic experiments on adults. For exam- public good game. ple, Grusecwx 1982 uses mother’s reports We begin by discussing the design of the about children’s home behavior. The experi- public good experiments in Section II. Sec- ments often ask subjects to make hypotheti- tion III gives the data and results. Section IV cal choices rather than choices with real discusses the dictator game, and Section V consequences and seldom incorporate repe- concludes. HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 97

II. PUBLIC GOODS EXPERIMENT DESIGN and the pooled contents were then doubled In each of the experiments reported be- Žor quadrupled, for the high-MPR treat- low, children were randomly assigned to ment. . The contents of the bowl were then groups of six. Two treatments were used. For evenly divided among the group members the first treatment, ␣ was set at 2, making and returned in the envelopes.Ž Fractional for a marginal private return to the donor payoffs were made in red chips worth one- Ž.MPR of one-third of a token for every third of a white chip.. They were then asked token contributed. For the second treatment, to count out the returned tokens and place ␣ was set at 4, making for a MPR of two- them in their cup. When this was done, we thirds. We call these the low-MPR and high- distributed five new tokens to each partici- MPR treatments, respectively. Participants pant and started the next round. were first through seventh-graders recruited We emphasized that each token they con- at after-school and summer recreational pro- tributed to the group would result in every grams in Albuquerque, New Mexico. person in the group getting one-thirdŽ two- Instead of cash, we gave our subjects an thirds in the high-return treatment. of a endowment of five white poker chips before token and that, therefore, contributing a to- each round. They were told that at the end ken would mean less for them personally but of the experiment they would be able to use more for the group. We also acted out two these tokens to purchase goods such as fancy different scenarios, showing that, when ev- pencils, small stuffed animals, super balls, eryone donated, the group got more but that and toy airplanes from a store that we set up any one member could do even better by not at the site. The exchange value of one token donating. While our subjects probably have was about 10 cents. In what can only be less cognitive ability than the typical under- described as a very successful effort to in- graduate subjects, we believe that these in- crease the salience of the rewards, subjects structions were substantially clearer, particu- were shown the goods available at the store larly about the rewards to free-riding, than in advance. Using tokens and a store seems usual. particularly suitable with younger children, We conducted two basic sets of these ex- who may have trouble converting cash into periments. The first set was conducted at five goods.Ž A large majority of parents reported schools, with between 17 and 23 children that there was no neighborhood store at participating at each. In these experiments, which their children were able to shop unsu- the children were not told how many repeti- pervised.. Since, according to the surveys, tions would be conducted, and the actual our subjects averaged about $2 in weekly number conducted varied from four to eight. allowance, the payoffs involved were quite When the number of children was not divisi- large in relative terms. Our subjects typically ble by six, we constructed a synthetic group doubled or tripled their disposable incomes for the extra subjects, using the decisions of for the week. members of another group to determine to- The subjects were seated behind parti- tal contributions for the synthetic group. tions and were assured that all their actions The second set of experiments was con- would be confidential and that we would ducted at eight different schools, with be- never disclose who was in what group. They tween 12 and 23 subjects participating at were given a cup to keep their earnings in each school. In these experiments, when the and a padded manila envelope marked with number of subjects was not divisible by six, their identification number to be used for the extra subjects were allowed to partici- contributions. At the beginning of each pate, but the data were not used. Subjects round, their five-chip endowments were were told in advance that there would be 10 placed in front of them, and they then placed repetitions and were reminded again just 1 the chips they wanted to keep in their cup before the last iteration. and the chips they wanted to contribute in the envelope. After each round, the en- velopes were collected, the contents were 1. We exclude data from two additional sites be- cause the number of subjects present, five and seven, poured into a bowl along with the contribu- was too small to ensure any degree of anonymity regard- tions from the other members of their group, ing group membership. 98 ECONOMIC INQUIRY

III. LINEAR PUBLIC GOOD EXPERIMENTS: of behavior across experiments. Inconsis- DATA AND RESULTS tency would suggest that our subjects are We use these data to address four basic confused by one or the other protocol or questions. First, we compare overall contri- that the protocols test different things. butions by children with contributions by adults, as reported by other researchers. Next we ask whether observable characteristics of First-Round Contributions the subjects are associated with altruistic be- havior. To do this, we concentrate on contri- First-round contributions are the simplest to analyze, since there is no previous behav- butions in the first round of each experi- 4 ment. These may be the clearest measures of ior to consider. Table I shows the frequency altruistic taste, since contributions are not distribution for first round donations. Only influenced by results of previous rounds.2 about 16% of the subjects contribute zero, Where possible, we use data from both sets while about 12% contribute the maximum of experiments in this part of the article.3 possible five tokens. Table II shows basic The results are reported below. summary data for each of the 12 sites from Then we look at behavior across iterations which we use the data, ordered by MPR. The in order to ask whether children learn to distribution of contributions are comparable free-ride. For this analysis, we use only the to those from experiments on adults. Mean data from the second set of experiments, first-round contributions for subjects at sites because these all had 10 iterations and a with the higher marginal private return were preannounced ending, as is typical with the 0.47 tokens, or 24% higher than those for those at sites with the low MPR. This dif- experiments others have done on adults. We ference, which Ledyardwx 1995 calls one of also excluded the data from the synthetic the ‘‘strong effects’’ to be found in public groups, because the subjects in these groups goods experiments, is significant at the 0.05 were not interacting with each other. These probability level using a t-test. results are reported below. Although we are encouraged at finding Last, in Section IV, we compare behavior this effect with children, we cannot reject the in the revealed preference public good ex- hypothesis that it is the result of uncon- periment with that in the voluntary contribu- trolled differences between the subjects. Ob- tions public good experiment. This compari- viously there is a substantial amount of vari- son is based on data from the three sites ation in contributions that is unrelated to the where we collected both types of data. Our MPR. We use regressions in order to control objective here is to address the consistency

4. We combine the data from both sets of experi- 2. However, this is also the round that is most likely ments for most of this analysis. To account for the to be susceptible to subject confusion, and so below we possibility that the lack of a defined end point affected examine similar questions for all rounds. first-round behavior, we ran the regressions with an 3. Since we collected somewhat different sets of indicator variable for the experiment set. This variable survey data for the different sets of experiments, some was insignificant, and the coefficients on the other vari- regressions use only data from one set of experiments. ables changed very little.

TABLE I Frequency Distribution for First-Round Contributions Ž.n s 208 Contribution ␮ Frequency Percentage 03416 14421 26230 33115 4126 52512 HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 99

TABLE II Descriptive Data and First-Round Contributions by Site First-Round Contributions Site MPR Subjects Rounds Mean Standard Deviation 11r3 24 6 2.2 0.88 31r3 17 4 2.2 1.4 51r3 24 8 1.7 1.7 71r3 18 10 1.8 1.5 81r3 18 10 2.4 1.6 10 1r3 12 10 0.75 0.87 13 1r3 12 10 1.8 1.5 14 1r3 12 10 2.1 1.9 Low-MPR average 1.9 1.5 22r3 17 6 2.4 0.79 62r3 18 10 2.4 1.4 92r3 18 10 3.0 1.8 12 2r3 18 10 1.8 1.8 High-MPR average 2.4 1.6 Overall average 2.1 1.5

for some possible sources of this variation, contribution plus one.5 Those independent and to examine what sorts of factors affect variables that are transformed are indicated donations. This use of regressions is rela- in Table IV. We also estimated the models tively rare in economic experiments, but it is using untransformed data, getting the same useful here because there is more variation signs on the statistically significant coeffi- in the characteristics of our subjects than is typical and because one objective of this 5. Because contributions are censored at zero and article is to see whether this variation is five, two-sided tobit would be a more appropriate statis- correlated with behavior. Table III shows tical procedure, both in these section and the subse- quent section which uses a panel of data to examine summary statistics for the variables we will behavior over iterations. Since to our knowledge there is use in the regressions, including some vari- no statistical routine available for calculating two-tailed ables we will use later in the paper. Table IV tobit for the panel data model, we report the OLS results here instead, for comparability. We ran these presents ordinary least squares results, with regressions using the tobit model, with very similar the dependent variable being the log of the results.

TABLE III Summary Statistics for Regression Variables Variable Observations Mean Standard Deviation Min Max Tokens shared, first round 208 2.1 1.5 0 5 High MPR site 208 0.34 0.48 0 1 Attendance 208 0.59 0.42 0 1 Age in years 201 8.8 1.6 5.6 14 Male 206 0.47 0.50 0 1 Number of siblings 189 1.4 0.92 0 5 Single parent family 111 0.25 0.44 0 1 Allowance in dollars per week 166 2.1 2.7 0 10 TV watching in hours per week 58 11 6.0 0 35 Church attendanceŽ times in an 58 1.1 1.8 0 8 average month. 100 ECONOMIC INQUIRY

TABLE IV First Iteration Contributions: OLS Regression Results Regression Variable 1 2 3 High-MPR indicator 0.16* 0.18 0.044 Ž.0.078 Ž. 0.11 Ž. 0.12 Attendqq 0.065** 0.082** 0.10 Ž.0.019 Ž. 0.025 Ž. 0.078 Age in yearsq 0.083 y0.27 Ž.0.27 Ž. 0.35 Male indicator y0.13 y0.032 Ž.0.11 Ž. 0.12 Number of siblingsqq 0.12 0.35 Ž.0.12 Ž. 0.22 Single parent household indicator 0.0034 Ž.0.12 Allowanceqq 0.091 Ž.0.085 TV watchingqq 0.021 Ž.0.094 Church attendanceqq 0.082 Ž.0.091 N 208 111 55 Adjusted r-squared 0.062 0.094 y0.040

Notes: Standard errors in parenthesis. An asteriskŽ. * means significant at the 5% level; a double asterisk Ž ** . at 1%; a plus sign Ž.q indicates log of value; a double plus sign Žqq .indicates the log of value plus one, to allow for zeros. cients, with generally somewhat less signifi- all the sites, n for this regression and the cance. subsequent one are smaller than in the first The first regression includes an indicator regression.. Subject’s age, gender, number of variable for the high MPR sites as well as a siblings, and an indicator variable for single- measure of the proportion of all the years of parent families all are statistically insignifi- schooling a subject has had that were at the cant. We also estimated this model using school where the experiment was conducted. indicator variables for birth order and only We use this as a measure of group attach- child, allowance, and measures of family in- ment, or at least of familiarity with the other come and mother’s education. None of these subjects in the experiment. We set this vari- variables had a significant effect. In regres- able to zero for the summer program stu- sion 3 we added descriptive variables that dents, since students often enroll in these measured allowance, TV watching, and programs somewhere other than their regu- church attendance.6 None of these was sig- lar schools, and they attend somewhat irreg- nificant. We also did not find significant ularly. In addition, these programs had been effects with measures of participation in or- in session less than two weeks when these ganized sports and other organized group experiments were conducted. This measure activities, such as Boy or Girl Scouts. Re- of group attachment has a positive and sta- gressions that included variables measuring tistically significant effect on first-round con- day care attendance at various ages showed tributions. At the mean of the high MP that these had no effect on contributions. variable, moving from 25% to 75% atten- The only variables for which we find sig- dance increases contributions by 0.2 tokens. nificant effects on first-round contributions In regression 2 we add some variables are the marginal private return and our mea- describing the basic demographic character- istics of the subject and their family.Ž Be- 6. These variables were only available for the obser- cause we were not able to collect this data at vations from the first set of experiments. HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 101 sure of group attachment. These variables cooperative behavior, such as church atten- both have the expected positive effects. The dance, have any effect on altruistic behavior first effect has been consistently found by in this experimental setting. others in adults, and the second effect has been documented with adults using experi- mental treatments, for example in Orbell, Beha¨ior across Iterations van de Kragt, and Daweswx 1988. To our knowledge however, no one has attempted to We now look at the pattern of donations find an equivalent effect with adults using a across iterations, in order to see whether measure of attachment developed outside the children learn to free-ride. We begin with experimental setting. descriptive statistics and then present regres- On the other hand, a host of other vari- sion results. Figure 1 shows how contribu- ables describing the subjects and their fami- tions change with iterations. Looking only at lies have no statistically significant effect on averages, there is little evidence that our contributions. Since most other public good subjects learn to free-ride during the experi- experiments have been conducted on rather ment. The general pattern is an initial in- homogeneous groups and have not at- crease in contributions, followed by a level- tempted to collect the sort of descriptive ing off and then a very slight decrease.7 Over variables that we have, we do not know to all sites, average contributions start at 2.1, what extent this second finding is specific to children. However, slight differences in con- increase to 3.2 in round 5, then fall to 3.0 by tributions by gender have been found for round 10. adults, e.g., in Andreoni and Vesterlund Figure 2 shows the percentage of subjects wx1997 . Here, we find no evidence that this giving each amount, for each iteration, with effect exists among children. Marwell and lower amounts toward the bottom of the Ameswx 1981 report that training in eco- nomics increases free-riding. Here we find no evidence that activities that might plausi- 7. This pattern was also observed in the data from bly be thought to promote and encourage the first set of experiments, so far as they went.

FIGURE 1 Mean Contribution for Different Sites, by Iteration 102 ECONOMIC INQUIRY

FIGURE 2 Percentage of Subjects Contributing Different Amounts, by Iteration

figure. From this figure, it is clear that the The general rise in contributions is at initial increase in contributions over the first odds with the large fall in contributions typi- five rounds comes from both an increase in cally, though not always, found with adult the number of subjects contributing and an subjects. On average, our subjects do not increase in the size of contributions from learn to free-ride. However, it is still possible those already contributing. The proportion that some subset of subjects does. While of subjects giving nothing falls from 19% in 50% of the subjects gave more in the last round 1 to 11% in round 5. From round 5 to three iterations than they gave in the first round 10, the proportion giving zero rises to three, 32% of them gave less. Still, it would 24%. However only three contributors give be a mistake to say that these subjects are zero every iteration. Most zero contributions necessarily free-riding, since random behav- come from small contributors switching to ior would also produce some subjects with and from zero. The percentage of subjects reduced contributions. However, since free- giving the maximum five tokens increases riding is typically found with adults, we hy- from 16% to 44% over the first five rounds pothesize that it should be more common and then stays near that level. One striking among our older subjects. We use a panel difference between first round and tenth data model with random effects to test this round contributions is the number of chil- hypothesis. This model allows for unob- dren contributing more than zero but less served heterogeneity in the propensity to 8 than five. In the first round, only about one- contribute. Descriptive statistics for the re- third of the subjects either keep all of their gression variables are in Table III, and the tokens or give all of them to the common results are in Table V. As in the regressions pool. By the tenth round, approximately on first-round contributions, the dependent two-thirds of the children are either keeping variable is the log of the contribution plus all of their tokensŽ. the Nash equilibrium or 8. Except in regression 3, the Hausman test cannot contributing all of themŽ the Pareto opti- reject the hypothesis that random effects, rather than mum.. fixed effects is appropriate for this data. HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 103

TABLE V Contributions Across Repetitions: Random Effects Regression Results Regression Variable 1 2 3 High return site 0.20* 0.21* 0.26** Ž.0.082 Ž. 0.085 Ž. 0.084 Iterationq 0.077** 0.66** 0.56** Ž.0.018 Ž. 0.20 Ž. 0.21 AttendŽ percentage of all school 0.054** 0.054** 0.077** at this school.qq Ž.Ž.Ž. 0.019 0.019 0.020 Ageq 0.53* 0.44 Ž.0.25 Ž. 0.26 Ageqq iteration interaction y0.27** y0.23** Ž.0.093 Ž. 0.098 Male y0.066 Ž.0.085 Number of siblingsqq 0.067 Ž.0.099 Allowanceqq 0.008 Ž.0.054 Single parent household y0.13 Ž.0.099 Constant 0.86** y0.29 y0.19 Ž.0.072 Ž. 0.55 Ž. 0.58 n 126 124 111 r-squared: Within 0.015 0.022 0.017 Between 0.12 0.12 0.21 Overall 0.073 0.077 0.12 P-value for Hausman test of RE 1.0 1.0 1.0

Notes: Standard errors in parenthesis. An asteriskŽ. * means significant at the 5% level; a double asterisk means significant at the 1% level; a plus sign Ž.q indicates log of value; a double plus sign indicates the log of value plus one, to handle zeros.

one, and independent variables are trans- mated these models using untransformed formed as noted. data, getting the same signs on the statisti- Regression 1 considers the effects of the cally significant coefficients, and generally MPR, the iteration number, and the atten- somewhat less significance. We also ran a dance measure. All are positive and signifi- model with both linear and quadratic terms cant. Regression 2 adds age, and an age- for round, with similar results. round interaction term. Age is significant In general, these results corroborate those and positive, while the interaction effect is in the first-round-only analysis. With the ex- significant and negative, indicating that, al- ception of group attachment and now age, though older children are initially more gen- and the age round interaction term, none of erous than younger ones, they also learn to the variables describing subjects and their free-ride more quickly. Regression 3 adds families had any explanatory power. We do some subject characteristics as in the first- find that the variables altered during the round regressions. Again, neither gender, the experiments have explanatory power. The number of siblings, allowance nor single par- high-return variable remains positive, and in ent household has a statistically significant most of the regressions contributions in- effect on contributions. The age, round, and crease over rounds. The positive sign on interaction coefficients change only by small iteration suggests that, overall, children do amounts across regressions 1, 2, and 3. As in not learn to free-ride. In fact, the opposite the first-round-only regressions, we also esti- seems to be true, and they tend to give more 104 ECONOMIC INQUIRY over time. However the negative coefficient IV. REVEALED PREFERENCE EXPERIMENT on the age iteration interaction variable indi- As a check on the possibility that some of cates that the contributions from older chil- our subjects are fundamentally confused, and dren do decline with repetition. In short, like that the behavior we are observing is unre- adults, older children do learn to free-ride. lated to altruism, at three sites we followed The estimates from regression 2 show that the public good experiment with a second iteration has a negative effect on donations test of altruistic behavior.Ž Subjects were not for children 11.5 years old or older. For a informed that this would be done until after hypothetical 8 year old with characteristics the conclusion of the public good experi- that are at the means of the other variables, ment.. In this section, we discuss this re- our estimates predict that donations would vealed preference test. We then give within- increase by 0.2 tokens from the first to the subject comparisons of the results of the second round, and by 0.12 from the second revealed preference experiments with those to the third round. For a 14 year old, they from the public good experiments. predict decreases of 0.14 and 0.08, respec- The experiment, based on Andreoni and tively. An heroic extrapolation predicts that Millerwx 1998 , tests whether subjects’ choices 21 year olds would decrease their contribu- about how much to give to another person tions by 0.5 tokens from the first to the obey the axioms of revealed preference. To second round and by 0.28 from the second to the extent they do, we argue that their giving the third. behavior in this experiment is rational and It is tempting to conclude from the results therefore that it can be used to provide a of this section that young children are not check on behavior in the linear public goods only basically altruistic, but in fact that they experiment. are better than adults at maintaining mutu- The experiment is essentially a modified ally beneficial behavior. This may well be true, and one plausible reason for it might dictator game where each subject is given be social ties. The coefficient on the variable some tokens and an opportunity to pass measuring attendance is positive in both the some, all, or none to an anonymous partner. regressions on first-round contributions and The modification is that each subject is shown the regressions on all contributions. If chil- 11 possible budget constraints for this trans- dren in general have stronger social ties than fer, each with a different income and price do adults, they may be better at maintaining ratio. The budget constraints were selected mutually beneficial cooperation. However, an to have many integer bundles, and to cross in alternative explanation for our results is that many places. The constraints we used are the repeated linear public goods game may shown in Figure 3, and the bundles pre- be a poor method of measuring altruism. sented on the sheets are shown with dots. In the linear public goods game, mistakes We explain that only one randomly chosen cannot be distinguished from altruism. Be- transfer will actually be made and also that cause children are presumably more likely they will be on the receiving end of transfers, than adults to make mistakes, this experi- if any, from a different partner than the one ment should therefore tend to overestimate to whom they can give tokens. children’s altruism relative to that of adults. Since many of our subjects cannot do the One reason for repeating the game is to give math necessary to stay within a budget, we the subjects a chance to learn, with the idea presented the possible transfers visually. We that once they understand the game their prepared a separate sheet of paper for each actions will accurately represent their prefer- budget constraint, showing each of the possi- ences. However, it is apparent from the liter- ble integer combinations of tokens they could ature that it takes many iterations for adults keep for themselves and tokens they could to learn free-riding, and it seems likely that pass to their partner along that budget con- children have even more difficulty. The re- straint. Every child received the same 11 sult that donations decline with repetition pages, ordered randomly. Subjects were given for older children, but not younger ones, 11 star stickers, and were told to put one star may simply mean that older children learn on each page, placing the star in the box that more quickly with repetition than do younger showed the combination of tokens for them- ones. selves and tokens for their partner that they HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 105

FIGURE 3 Budget Sets with Available Bundles Indicated as Dots

liked best. The subjects seemed to under- the subject wasted by failing to choose ratio- stand this procedure very well. nally. For example, a AEI of 0.75 means that the cheapest available bundle that would have satisfied the axioms of revealed prefer- Re¨ealed Preference Results ence would have cost only 75% as much as Using an algorithm based on Varian the bundle they actually chose, which did not wx1995 , we counted the number of violations satisfy the axioms. We used the incomes and prices implicit in the budget sets to construct of the generalized axiom of revealed prefer- 9 enceŽ. GARP found in each child’s eleven this measure. choices. A violation of GARP occurs when a In addition to checking for GARP viola- subject picks a bundle of goods x when they tions, we compute a simple measure of the could have picked another bundle xЈ that willingness to share in this experiment. The they have indirectly revealed they preferred measure, which we call ‘‘proportion shared,’’ to x. Bundle xЈ is directly revealed preferred is simply the average over the 11 constraints to x if xЈ is chosen when x, or some other of the number of tokens in the chosen bun- bundle with more of at least one good than dle that go to the partner, divided by the x, is in the choice set, and xЈ is indirectly total number of tokens in the bundle. Sum- revealed to be preferred to x when some chain of directly revealed choices leads from xЈ to x. In addition to just counting the violations, we calculated their severity using Afriat’swx 1972 efficiency index, or AEI. This 9. Because these choice sets are discreet, rather index ranges from zero to one. The amount than continuous, this measure potentially exaggerates the severity of violations, since the subject might have by which the index falls below one can be actually chosen a bundle with a higher AEI, had it been thought of as the proportion of income that available in the choice set. 106 ECONOMIC INQUIRY

TABLE VI Revealed Preference Summary Statistics Variable Mean Standard Deviation Min Max All subjectsŽ. 40 observations : Violations 2.2 3.0 0 11 AEI 0.87 0.20 0.33 1 Proportion shared 0.29 0.25 0.0 0.98 ‘‘Rational’’ subjectsŽ. 28 observations : Violations 0.43 0.82 0 2 AEI 0.97 0.049 0.875 1 Proportion of tokens shared 0.22 0.24 0 0.98

mary statistics for this measure are given in On average, they picked bundles where they Table VI along with those for the number of shared 22% of the available tokens, com- violation and the AEI. pared to an average for all subjects of 29%. The average number of violations is 2.2, We tested whether the demographic and and the average severity of the violations is other characteristics that we had tried in the 0.87. We ran computer simulations picking previous regressions to explain public good bundles randomly and found an average of contributions could explain altruism in this 5.7 violations and a severity index of 0.65. protocol. None of these variables had statis- Our sample was skewed: 22 subjects had no tically significant effects on the proportion violations. Clearly our subjects are not shared in this experiment.Ž The school atten- choosing randomly. We regressed age and dance variable did not vary over these sub- gender on the number of violations and the jects, all of whom were at summer programs.. AEI, and neither variable was significant. Table VII shows the results we obtained We arbitrarily classify the 28 subjects with when we regressed these dictator game re- AEI scores of 0.875 or above and no more sults on contributions in the public good than two violations as ‘‘rational.’’10 These experiment, using two-sided tobit to account subjects averaged 0.43 revealed preference for the fact that contributions must be be- violations and had an average AEI of 0.97. tween 0 and 5. We only use the 28 ‘‘rational’’ subjects in these regressions. We run this 10. Running the regressions with all 40 subjects gave regression with two different dependent vari- similar results. ables: the amount shared in the first round

TABLE VII Regressions Using Revealed Preference Results Regression 1 Regression 2 Dependent Variable Dependent Variable 1st-Round 10th-Round Independent Variable Contribution Contribution Tokens shared divided by 6.8** 11.3 all tokens in bundleŽ. 2.4 Ž. 5.9 n 28 28 Pseudo r-squared 0.086 0.027

Notes: Standard errors in parenthesis. An asteriskŽ. * means significant at the 5% level; a double asterisk Ž ** . means significant at 1%. HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 107 of the public good experiment and the is zero contributions, this general downward amount shared in the last round. The results trend is a comforting tendency, suggesting show that behavior in the dictator game is that the subjects are at least converging to- related to behavior in the first round of the ward a Nash equilibrium. In our experi- public good experiment, but not in the last ments, we observe increasing contributions, round, although neither r-squared is particu- the wrong direction from the point of view of larly high. Note that the dictator game im- most learning models. One plausible expla- mediately followed the last round of the pub- nation for this behavior is that younger chil- lic good experiment. dren mistakenly view their contributions as We propose the following interpretation investments with high rates of return, of these results, which we believe is also whereas older children learn to free-ride, as consistent with the results of the public good adults do. experiment. Behavior in the first round of However, despite their difficulty learning the public good experiment is to some extent to free-ride, we argue that even young chil- driven by altruism, though there also seems dren clearly do have a taste for altruism. to be a significant amount of confusion. While with adults the confusion generally is Even in the dictator game, they give an aver- reduced with repetition, and the less altruis- age of 29% of their tokens away. Further- tic subjects start to free-ride once they un- more, their choices about how many tokens derstand the true incentives, many children to give away generally, though not always, simply get more confused with repetition. By change rationally in response to changes in the last round, the behavior of a significant their incomes and the price of giving. This is fraction of the subjects is driven by confu- true both across subjects in the public good sion. In the subsequent, simpler, revealed experiment and within subjects in the dicta- preference experiment, that confusion is tor game. Similarly, children with longer at- eliminated. Subjects who gave large amounts tendance at the same school give more. Still, in the last round of the public good experi- children’s preferences about altruism do ment were not generous in the subsequent seem substantially less well formed than do revealed preference game. However, we adults. Although their results are not directly should note that another interpretation is comparableŽ we use more budget constraints, that the children are acting optimally in the each with fewer choices. Andreoni and Miller public goods game by building cooperative wx1998 find that only 13 of 142 adult subjects behavior and that in the subsequent dictator had any GARP violations, while 18 of our game, since there are no opportunities for 40 subjects did. further cooperation, they then reduce their We believe that the finding that primary contributions. school children act in a way that is not drastically different than that of adults is V. CONCLUSION robust and somewhat surprising. Retrospec- tion alone is enough to convince most people We find that first-round contributions by that other sorts of behaviors change drasti- children, both in terms of the mean and the cally between childhood and adulthoodᎏ variation, are in line with those that others have found with adults. This is encouraging, choice over time, for example. However, on especially since age has only a small effect. further thought, it seems appropriate that The marginal private return and a measure the altruistic behavior of children would be of group attachment have positive effects on similar to that of adults: both live in very these contributions. Other subject and par- social environments with repeated interac- ent demographic variables explain none of tions with others and with many opportuni- the variation in these contributions. ties for others to observe their behavior and The overall increase with repetition is reward or punish them for it. Our subjects the opposite of that generally found in are already old enough to have received a other experiments: one of the stronger ef- large amount of encouragement to engage in fects that those studying adults have found is sharing activities, and have experienced the that contributions fall with repetition. Since advantages, and disadvantages, of altruism in the Nash equilibrium for these experiments many different settings. 108 ECONOMIC INQUIRY

APPENDIX Let’s try that again. So, what if I get these six EXPERIMENTAL PROTOCOLS envelopes back?Ž Experimenter dumps out six envelopes that have 0, 1, 1, 0, 3, 0 tokens in them.. OK, now there LINEAR PUBLIC GOOD PROTOCOL are five tokens in this group’s pile, so I add three more five times. Now there’s 20 in the pile. Each kid gets 3 We first had the subjects gather around a table and read the back, and I have 2 left over. See these red tokens? following instructions to them. Three reds equal one white. So I am going to make some change, just like 5 pennies make one nickel. We are going to play a game. By playing the game, Ž.Count out, 3 reds for each white Now I have six reds, you will earn tokens that you can use to buy things at so each kid can get one. I will put 3 whites plus 1 red in our store.Ž. Show store. Each white token that you get each envelope. during the game is worth about 10 cents, and in addition Remember: If you get a red one back, it means just you may get some red tokens that are worth about 3 part of a white one. ALL the kids in each group get cents. Pay very careful attention to these instructions, back exactly the same number of tokens, no matter how because the better you understand them the more to- many they share or keep. Notice that the kids who kens you can earn, and the more tokens you have the shared nothing got just as many tokens back as the kid more things you will be able to buy. If you have ques- who shared 3. tions raise your hand. Otherwise, please be quiet and We then had the subjects sit down at tables, with tri-fold listen carefully, just like you would to your teacher in partitions for pri¨acy, and read them following. school. You will get 10 turns at the game. At the beginning There are five white tokens at your place. These of each turn we will give you 5 white tokens, and you tokens belong to you. You may keep all of them if you may get more tokens at the end of each turn, depending want, or you can share some or all of them with your on your decisions and the decisions of the people in group. We do not think it would be better to share or to your group. Remember, the more tokens you have at keep, we are just interested in what you decide to do. the end, the more stuff you can buy, so pay careful Decide how many tokens you want to keep and put attention to these instructions! You are going to be in a them in your cup. Put the number of tokens you want to group with 5 other kids. You will be in the same group share in your envelope. When you are ready raise your during the whole experiment. We are not going to tell hand so a helper can pick up your envelope. Don’t let you who is in which group, and we aren’t going to tell anyone else see how many you are sharing or keeping! anyone else who is in your group. We are going to keep Remember: For every token that you and the other this a secret even after the experiment is over, so no one kids in your group share, I will add 3 more tokens. Then will ever know. I will divide all the tokens up equally. If you get a red You get to decide whether you are going to keep one back, it’s as if I tried to divide up a white token in your tokens or are going to share them with your group. three parts. We do not think it would be better for you to share the Remember: You might get back more than you tokens or better to keep them. No one will know how shared, but you might get back less. It all depends on what the other kids in your group do. many you shared or how many you kept or whether you shared or not. Keep your decision a secret: you are not We then collected the en¨elopes, recorded the contribu- allowed to ask other kids what they did, or tell them tions, and passed back the earnings. The following was what you did. If you do, we may come and take a token read after each subsequent round. away from you! You will be sitting at these desks. Each desk will OK, now let’s play another turn. A helper will give have a ‘‘keeping cup’’ and a brown envelope in front of you back your envelope with the tokens you get from it. The keeping cup is for your tokens, and the envelope your group’s pile, and another helper will give you five is for the ones that you want to share. At the beginning new tokens. You can’t share any of the tokens that you of each round, we will give you 5 new tokens. You will get back in your envelope, so count them, quietly, and put the ones that you want to share in your envelope, then put them in your cup right away. You can share as and the ones that you want to keep in your cup. You many of your new tokens as you want to. Raise your can share any number of tokens, from zero to 5. The hand when you’re ready to have your envelope picked partitions are there so that you can keep your choice a up. The same five other kids are still in your group. They don’t know whether you are in their group, or how secret. When everybody has made their choice we will many you shared last time. collect all the envelopes. Now, I will tell you how the sharing works. I will add After the ninth round, we also read the following. 3 more tokens for every 1 that kids share. So, what if I get these six envelopes back?Ž Experimenter then dumps The game is almost over. You have only one more out six envelopes that have one token each. See, each turn to play this game. envelope had one token in it. Now there are six tokens After the tenth round, we read this. in this group’s pile.Ž Experimenter then counts out the ones that are added.. Now there are 24 in the pile. So We hope you enjoyed the game. Now we want you to now I need to split this up to the six kids: each one gets start counting out your tokens. We will hold up the four tokens back. I will put 4 tokens in each envelope, things from the store one at a time. If you want to buy and deliver them back. These kids would then put the something, hold up your hand and we will bring it tokens in their keeping cups. around to you. Thanks for helping us. HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 109

GARP PROTOCOL Remember: I might pick the ticket for any page from my hat. So pick the box carefully on every single piece The GARP experiment was performed before subjects were of paper. allowed to buy things from their public good experiment earnings. Subjects remained seated at the stations used in We then drew a ticket from the hat, paid the subjects and the public goods experiment, and we read the following partners accordingly, and allowed them to spend the tokens instructions to them. as described abo¨e. This is a game that gives you a chance to share with another person. We are interested in finding out what you want to doᎏthere is no ‘‘right’’ thing to do, just do REFERENCES whatever makes you feel best. Afriat, Sidney. ‘‘Efficiency Estimation of Production The game is pretty complicated, so pay careful atten- Functions.’’ International Economic Re¨iew, Octo- tion. The tokens that you get can be used to buy things ber 1972, 568᎐98. from our store, just like in the last game. Remember that the more tokens you get the more you can buy at Andreoni, James. ‘‘Cooperation in Public-Goods Exper- the store. iments: Kindness or Confusion?’’ American Eco- ¨ ᎐ The game works like this. We will match you with 2 nomic Re iew, September 1995, 891 904. other kids here today. We are not going to tell you who Andreoni, James, and John Miller. ‘‘Giving According they are, and we aren’t going to tell them who you are. to GARP: An Experimental Study of Rationality It will be impossible for any kid to ever know this. One and Altruism.’’ Social Systems Research Institute of these kids is your ‘‘giving partner’’ and the other kid Working Paper 9902, University of Wisconsinᎏ is your ‘‘getting partner.’’ Madison, 1998. We are giving each one of you a packet with 11 Andreoni, James, and Lise Vesterlund. ‘‘Which Is the pages.Ž. Pass these out. Turn over the first sheet, and Fair Sex? Gender Differences in Altruism.’’ Social look at the next page. Each page has some boxes on it. Systems Research Institute Working Paper 9810, Each box has some circles and some squares in it. The University of WisconsinᎏMadison, 1998. circles stand for tokens that will go to you, and the Eisenberg, Nancy, and Paul H. Mussen. The Roots of squares stand for tokens that will go to your giving Prosocial Beha¨ior in Children. Cambridge: Cam- partner. On each page, you will pick just one of these bridge University Press, 1989. boxes. Remember: circle tokens, if any, will go to you, and square tokens, if any, will go to your ‘‘giving part- Grusec, Joan E. ‘‘The Socialization of Altruism,’’ in The ¨ ¨ ner’’. Your ‘‘getting partner’’ will also be picking a box, De elopment of Prosocial Beha ior, edited by Nancy and so you will also get the square tokens, if any, from Eisenberg. New York: Academic Press, 1982, 139᎐66. the box that your ‘‘getting partner’’ chooses. Seeᎏyou have a partner and you are also someone else’s partner. Ledyard, John O. ‘‘Public Goods,’’ in The Handbook of Remember, each token is worth about 10 cents. So, Experimental Economics, edited by John H. Kagel if you choose a box likeŽ. it’s just like keeping Ž. for and Alvin E. Roth. Princeton, N.J.: Princeton Uni- ᎐ yourself, and givingŽ. to your ‘‘giving partner.’’ And if versity Press, 1995, 111 94. your getting partner chose this box, then he would get Marwell, Gerald, and Ruth E. Ames. ‘‘Economists Free Ž.and you would get Ž. . Ride, Does Anyone Else?’’ Journal of Public Eco- You pick a box by taking one of your stickers and nomics, June 1981, 295᎐310. putting it in whichever box you want to. But remember, Orbell, J., A. van de Kragt, and R. Dawes. ‘‘Explaining you only have one sticker for each page, so you can only Discussion Induced Cooperation.’’ Journal of Per- choose one box on each page. You have to put just one sonality and Social Psychology, May 1988, 811᎐19. sticker on each piece of paper. If you don’t do this, you might not get any tokens. Palfrey, Thomas, and Jeffrey Prisbrey. ‘‘Anomalous Be- However, while we want you to make a choice on havior in Linear Public Goods Experiments: How Much and Why?’’ American Economic Re¨iew, every page, the game is a little more complicated. After December 1997, 829᎐46. everybody has picked one box from each piece of paper, we will put a ticket for each page in my hat and I will Peters, H. Elizabeth, A. Sinan Unur, Jeremy Clark, and close my eyes and pick out one ticket. That is going to William Schulze. ‘‘Free-Riding and the Provision decide which page we are going to give tokens for. You of Public Goods in the Family: An Experimental will get the round tokens, if any, from the box you Test of the Rotten Kid Theorem’’. Cornell Depart- picked on that page, and the square tokens, if any, from ment of Economics Working Paper, 1997. the box that your ‘‘getting partner’’ picked on that page. Underwood, Bill, and Bert S. Moore. ‘‘The Generality The square tokens, if any, from the box that you picked of Altruism in Children,’’ in The De¨elopment of will go to your ‘‘giving partner.’’ Since nobody knows Prosocial Beha¨ior, edited by Nancy Eisenberg. New which ticket will come out of the hat, the best thing to York: Academic Press, 1982, 25᎐52. do is pick the box you like best on every single page. Varian, Hal. ‘‘Efficiency in Production and Consump- So there are two ways to get tokens: you get the tion,’’ Working Paper and Mathematica Notebook, round ones, if any, from the box that you choose, and 1995wx online . Available: ftp:rrftp.telospub.comr you will get the square ones, if any, from the box that pubr EconFinancer CompEconr wJanuary 12, your partner decides to give to you. 1999x .