CHILDREN'S ALTRUISM IN PUBLIC GOOD AND - Bill Harbaugh

15 Pages·1999·0.2 MB·English

CHILDREN’S ALTRUISM IN PUBLIC GOOD AND
DICTATOR EXPERIMENTS
WILLIAM T. HARBAUGH and KATE KRAUSE*
Weexaminethede(cid:1)elopmentofaltruisticandfree-ridingbeha(cid:1)iorin6(cid:1)12-year-old
children.We find that the le(cid:1)el of altruisticbeha(cid:1)ior in children is similar to that of
adultsbutthat repetitionhas a differenteffect.Youngerchildren’scontributionstend
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-roundcontributions. ŽJEL H41.
I. INTRODUCTION way similar to adults, the taste for altruism
Research on altruism among adults using must be,if notinnate, at least determinedby
linear public good experiments has estab- very early experiences. Next, since hetero-
lishedanumberofinteresting results. Adults geneity in altruistic behavior may be due to
areinitially farmoregenerousthan wouldbe 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. Theobserveddecline 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 confirmedby a widevariety ofbehav- 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 weexamine the behaviorof6-to12-year-
or about the protocol is age-related, we in-
old children in public goodexperiments.
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
nally, to test whether the linear public goods
adults. If even young children behave in a
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 NewMexico Research Allocation Committee
subset of the original subjects.
and the National Science Foundation. We thank Jim
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
groups of N members, where N is generally
of Albuquerque recreation program leaders for their
help organizing and conducting these experiments, and between 4 and 10. Subjects play either a
togiveourthankstothechildrenwhoparticipated. preannouncedorrandomlydeterminednum-
Harbaugh: Assistant Professor, Department of Eco- ber of rounds. At the beginning of each
nomics, University of Oregon, Eugene, Oregon
round, subjects are endowed with experi-
97403-1285, Phone [phone], Fax [phone],
[email protected] ment currency that is exchanged for cash at
Krause:Assistant Professor, Department ofEconomics, the end of the experiment. They then must
1915 Roma NE, University of New Mexico, Albu-
decide whether to keep it or to contribute
querque, New Mexico 87131-1101, Phone 505-277-
3429,Fax[phone],[email protected] any portion of it to the group. The money
95
EconomicInquiry
ŽISSN0095-2583.
Vol.38,No.1,January2000,95(cid:1)109 (cid:1)WesternEconomicAssociationInternational
96 ECONOMIC INQUIRY
given to the group is multiplied by a number tition. In contrast, the experiments wereport
(cid:2) 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 environmentthatprovidedforanonymityand
members. In this game, the individually ra- real consequences, making them very similar
tional strategy Žfor 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. goodexperiment to estimate altruism is that,
(cid:2) (cid:3)
Ledyard 1995 providesmoreinformation 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 (cid:2)(cid:4)N Žthe marginal private that subjects’ mistakes would be reduced by
return.islarger,andthat donationsdecrease 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
(cid:2) (cid:3)
whelmingmajorityofthese experiments have earnings,Andreoni 1995 alters thestandard
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
(cid:2) (cid:3) (cid:2) (cid:3)
Marwell and Ames 1981 used high school Prisbey 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
(cid:2) (cid:3)
1997, 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 dodecline 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 implementwithchildren,wedidrunasimple
altruistic behaviorofchildren.Eisenberg and test ofthe consistency ofthe behavior of our
(cid:2) (cid:3)
Mussen 1989 has a good review of this. subjects across two different protocols. At
(cid:2) (cid:3)
Underwood and Moore 1982 report that three sites, we followed the public good ex-
age has generally been foundtobe positively periment by having children play a simple
correlated with both frequency and levels of dictator game, modeled after Andreoni and
(cid:2) (cid:3)
contributions. They also note that gender Miller 1998, that asked them to make do-
has been found to be correlated with gen- nate(cid:4)keep 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-
Themethodologyused in studies bydevelop- asedineither direction.So,behaviorinthese
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 goodgame.
(cid:2) (cid:3)
ple, Grusec 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- tionIII givesthe dataandresults. SectionIV
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
groupsofsix.Twotreatments wereused.For evenly divided among the group members
the first treatment, (cid:2) was set at 2, making and returned in the envelopes. ŽFractional
for a marginal private return to the donor payoffs were made in red chips worth one-
ŽMPR. of one-third of a token for every third of a white chip.. They were then asked
tokencontributed.Forthe secondtreatment, to count out the returned tokens and place
(cid:2) 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-MPRand 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 emphasizedthat each token they con-
at after-school andsummerrecreational pro- tributed to the group would result in every
grams in Albuquerque, New Mexico. person in the group getting one-third Žtwo-
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 wouldmean 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 topurchase goodssuch as fancy different scenarios, showing that, when ev-
pencils, small stuffed animals, super balls, eryone donated,the groupgot more but that
and toyairplanes froma store that weset up any one member coulddoeven 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.Thefirstset wasconductedat five
goods. ŽA 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
placedinfrontofthem,andtheythen placed repetitions and were reminded again just
the chips they wanted to keep in their cup before the last iteration.1
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-
wastoosmalltoensureanydegreeofanonymityregard-
tionsfromthe othermembersoftheir group, inggroupmembership.
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,asreportedbyotherresearchers.Next
we ask whether observable characteristics of First-RoundContributions
the subjects are associated with altruistic be-
First-round contributions are the simplest
havior. To do this, we concentrate on contri-
to analyze, since there is no previous behav-
butions in the first round of each experi-
iortoconsider.4 TableIshowsthe frequency
ment.Thesemaybethe clearest measures of
distribution for first round donations. Only
altruistic taste, since contributions are not
influenced by results of previous rounds.2 about 16% of the subjects contribute zero,
while about 12% contribute the maximum
Where possible, we use data from both sets
of experiments in this part of the article.3 possible five tokens. Table II shows basic
summary data for each of the 12 sites from
The results are reported below.
whichweusethedata,orderedbyMPR.The
Thenwelookatbehavioracrossiterations
distribution of contributions are comparable
in order to ask whether children learn to
to those from experiments on adults. Mean
free-ride. For this analysis, we use only the
first-round contributions for subjects at sites
data from the second set of experiments,
with the higher marginal private return were
because these all had 10 iterations and a
0.47 tokens, or 24% higher than those for
preannounced ending, as is typical with the
those at sites with the low MPR. This dif-
experiments others have done on adults. We (cid:2) (cid:3)
ference, which Ledyard 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 withchildren,wecannotrejectthe
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
ationincontributions that isunrelated tothe
where we collected both types of data. Our
MPR.Weuse regressions in ordertocontrol
objective here is to address the consistency
4. We combine the data from both sets of experi-
2. However,thisisalsotheroundthatismostlikely ments for most of this analysis. To account for the
tobesusceptible tosubjectconfusion,andsobelowwe possibility that the lack ofa definedendpointaffected
examinesimilarquestionsforallrounds. 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 wasinsignificant,andthecoefficientsontheothervari-
regressions useonlydatafromonesetofexperiments. ableschangedverylittle.
TABLEI
FrequencyDistributionforFirst-RoundContributionsŽn(cid:5)208.
Contribution(cid:1) Frequency Percentage
0 34 16
1 44 21
2 62 30
3 31 15
4 12 6
5 25 12
HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 99
TABLEII
DescriptiveDataandFirst-RoundContributionsbySite
First-RoundContributions
Site MPR Subjects Rounds Mean StandardDeviation
1 1(cid:4)3 24 6 2.2 0.88
3 1(cid:4)3 17 4 2.2 1.4
5 1(cid:4)3 24 8 1.7 1.7
7 1(cid:4)3 18 10 1.8 1.5
8 1(cid:4)3 18 10 2.4 1.6
10 1(cid:4)3 12 10 0.75 0.87
13 1(cid:4)3 12 10 1.8 1.5
14 1(cid:4)3 12 10 2.1 1.9
Low-MPRaverage 1.9 1.5
2 2(cid:4)3 17 6 2.4 0.79
6 2(cid:4)3 18 10 2.4 1.4
9 2(cid:4)3 18 10 3.0 1.8
12 2(cid:4)3 18 10 1.8 1.8
High-MPRaverage 2.4 1.6
Overallaverage 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-sidedtobitwouldbeamoreappropriatestatis-
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
behavioroveriterations.Sincetoourknowledgethereis
use in the regressions, including some vari- nostatistical routineavailableforcalculating two-tailed
ables wewilluse later in the paper.TableIV 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.
TABLEIII
SummaryStatistics forRegressionVariables
Variable Observations Mean StandardDeviation Min Max
Tokensshared,firstround 208 2.1 1.5 0 5
HighMPRsite 208 0.34 0.48 0 1
Attendance 208 0.59 0.42 0 1
Ageinyears 201 8.8 1.6 5.6 14
Male 206 0.47 0.50 0 1
Numberofsiblings 189 1.4 0.92 0 5
Singleparentfamily 111 0.25 0.44 0 1
Allowanceindollarsperweek 166 2.1 2.7 0 10
TVwatchinginhoursperweek 58 11 6.0 0 35
ChurchattendanceŽtimesinan 58 1.1 1.8 0 8
averagemonth.
100 ECONOMIC INQUIRY
TABLEIV
FirstIteration Contributions: OLSRegressionResults
Regression
Variable 1 2 3
High-MPRindicator 0.16* 0.18 0.044
Ž0.078. Ž0.11. Ž0.12.
Attend(cid:6)(cid:6) 0.065** 0.082** 0.10
Ž0.019. Ž0.025. Ž0.078.
Ageinyears(cid:6) 0.083 (cid:7)0.27
Ž0.27. Ž0.35.
Maleindicator (cid:7)0.13 (cid:7)0.032
Ž0.11. Ž0.12.
Numberofsiblings(cid:6)(cid:6) 0.12 0.35
Ž0.12. Ž0.22.
Singleparenthouseholdindicator 0.0034
Ž0.12.
Allowance(cid:6)(cid:6) 0.091
Ž0.085.
TVwatching(cid:6)(cid:6) 0.021
Ž0.094.
Churchattendance(cid:6)(cid:6) 0.082
Ž0.091.
N 208 111 55
Adjusted r-squared 0.062 0.094 (cid:7)0.040
Notes:Standarderrorsinparenthesis.Anasterisk Ž*.meanssignificantatthe5%level;adoubleasterisk Ž**.at
1%;aplussignŽ(cid:6).indicateslogofvalue;adoubleplussignŽ(cid:6)(cid:6).indicatesthelogofvalueplusone,toallowfor
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 proportionof 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 comeand mother’s education. Noneof 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 arethe marginalprivatereturn andourmea-
describing the basic demographic character-
istics of the subject and their family. ŽBe-
6. Thesevariableswereonlyavailablefortheobser-
cause wewere not able tocollect this data at vationsfromthefirstsetofexperiments.
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(cid:1)ior across Iterations
(cid:2) (cid:3)
van de Kragt, and Dawes 1988. To our
knowledgehowever,noonehasattemptedto We now look at the pattern of donations
find an equivalent effect with adults using a across iterations, in order to see whether
measureofattachmentdevelopedoutsidethe children learn to free-ride. We begin with
experimental setting. descriptivestatistics andthen 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
ingoffandthen averyslight 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
increase to 3.2 in round 5, then fall to 3.0 by
children. However, slight differences in con-
round 10.
tributions by gender have been found for
Figure 2 shows the percentage of subjects
adults, e.g., in Andreoni and Vesterlund
(cid:2) (cid:3) giving each amount, for each iteration, with
1997. Here, we find no evidence that this
effect exists among children. Marwell and lower amounts toward the bottom of the
(cid:2) (cid:3)
Ames 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 thefirstsetofexperiments,sofarastheywent.
FIGURE 1
MeanContributionforDifferentSites,byIteration
102 ECONOMIC INQUIRY
FIGURE 2
Percentage ofSubjectsContributingDifferentAmounts,byIteration
figure. From this figure, it is clear that the The general rise in contributions is at
initial increase in contributions over the first oddswith 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 tofree-ride.However,itisstill 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. Fromround 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
than five. In the first round, only about one- contribute.8 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 tokens Žthe Nash equilibrium. or
contributing all of them Žthe Pareto opti- 8. Except in regression 3,the Hausman test cannot
reject the hypothesis that random effects, rather than
mum.. fixedeffectsisappropriateforthisdata.
HARBAUGH & KRAUSE: CHILDREN’S ALTRUISM 103
TABLEV
ContributionsAcrossRepetitions:RandomEffects RegressionResults
Regression
Variable 1 2 3
Highreturnsite 0.20* 0.21* 0.26**
Ž0.082. Ž0.085. Ž0.084.
Iteration(cid:6) 0.077** 0.66** 0.56**
Ž0.018. Ž0.20. Ž0.21.
AttendŽpercentageofallschool 0.054** 0.054** 0.077**
atthisschool.(cid:6)(cid:6) Ž0.019. Ž0.019. Ž0.020.
Age(cid:6) 0.53* 0.44
Ž0.25. Ž0.26.
Age(cid:6)iteration(cid:6)interaction (cid:7)0.27** (cid:7)0.23**
Ž0.093. Ž0.098.
Male (cid:7)0.066
Ž0.085.
Numberofsiblings(cid:6)(cid:6) 0.067
Ž0.099.
Allowance(cid:6)(cid:6) 0.008
Ž0.054.
Singleparenthousehold (cid:7)0.13
Ž0.099.
Constant 0.86** (cid:7)0.29 (cid:7)0.19
Ž0.072. Ž0.55. Ž0.58.
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-valueforHausmantestofRE 1.0 1.0 1.0
Notes:Standarderrorsinparenthesis. Anasterisk Ž*.meanssignificantatthe5%level;adoubleasterisk means
significant at the 1%level; a plussign Ž(cid:6).indicates logofvalue; a doubleplussign indicates the logofvalue plus
one,tohandlezeros.
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 Ingeneral,these results corroboratethose
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
roundregressions.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
onthe ageiteration interaction variable indi- As a check on the possibility that some of
cates that the contributions from older chil- oursubjectsarefundamentallyconfused,and
drendodecline withrepetition.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
Theestimates fromregression 2showthat the public good experiment with a second
iteration has a negative effect on donations test of altruistic behavior. ŽSubjects 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 goodexperiments.
predict decreases of 0.14 and 0.08, respec-
The experiment, based on Andreoni and
tively. An heroic extrapolation predicts that (cid:2) (cid:3)
Miller 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
secondroundandby0.28fromthe secondto
the extent they do,weargue that their giving
the third.
behavior in this experiment is rational and
It is temptingtoconcludefromthe 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
dictator game where each subject is given
true, and one plausible reason for it might
some tokens and an opportunity to pass
be social ties. The coefficient on the variable
some, all, or none to an anonymous partner.
measuring attendance is positive in both the
Themodificationisthateachsubjectisshown
regressions on first-round contributions and
11 possible budget constraints for this trans-
the regressions on all contributions. If chil-
fer, each with a different income and price
dreningeneral havestronger social ties than
ratio. The budget constraints were selected
do adults, they may be better at maintaining
tohavemanyintegerbundles,andtocrossin
mutuallybeneficialcooperation.However,an
many places. The constraints we used are
alternative explanation for our results is that
shown in Figure 3, and the bundles pre-
the repeated linear public goods game may
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 theywillbeonthe receivingendoftransfers,
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 willaccurately represent their prefer- budget constraint, showingeach ofthe possi-
ences. However,it is apparent fromthe liter- bleintegercombinationsoftokenstheycould
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,orderedrandomly.Subjectsweregiven
for older children, but not younger ones, 11star stickers, andweretoldtoputonestar
may simply mean that older children learn oneach page,placingthe star inthe boxthat
morequicklywithrepetitionthandoyounger showed the combination of tokens for them-
ones. selves and tokens for their partner that they