JOURNAL OF
Journal of Economic Behavior and Organization
Vol. 25 (1994) 25-36
EconomicBehavior
& Organization
The influence of gender on the provision
of a public good
Clifford
Nowell
*, Sarah Tinkler
Department of Economics, Weber State University, Ogden, UT 84408-3807, USA
Received July 1993, final version received December 1993
Abstract
Previous researchers have obtained contradictory results concerning the influence of
gender on behavior in the experimental setting. One study finds women significantly less
cooperative than men (Rapoport and Chammah 1965), while another study finds women
and men equally cooperative, after frequent repetitions of a game (Mason, Phillips and
Redington 1991). We examine the influence of gender on public good provision in a
four-person game using all-female, all-male and mixed gender groups of undergraduates.
We find some evidence that all-female groups are more cooperative than either all-male or
mixed gender groups.
Economics of gender; Public economics; Public goods; Design of experiments; Laboratory
group behavior
Keywords:
JEL classification:
516; H41; C92
1. Introduction
The literature of experimental economics provides substantial documentation
that free riding in public goods experiments leads to significant underinvestment
in
the public good. Experimental evidence suggests that subjects initially contribute
forty to sixty percent of their stake in the public good and that this contribution
rate declines with repetition (Dawes and Thaler 1988). According to Roth, the
* Corresponding author.
0167-2681/94/$07.00
0 1994 Elsevier Science B.V. At1 rights reserved
SSDI 0167-2681(94)00048-J
26
C. Nowell, S. Tinkler/J.
ofEconomic Behavior & Org. 25 (1994) 25-36
debate has now shifted from ‘how much and under what conditions it [free riding]
occurs, to what mechanisms
and environments
may be most vulnerable
and
invulnerable
to its effects’ (Roth 1988, 997). Some authors have examined the
possibility that the gender of experimental subjects might influence experimental
outcomes.
The psychology literature offers some insight in this area. In experiments
requiring the division of a reward, Eagly (1987) reports that men seem to take
more for themselves than women do although men also appear to be more
interested in equity than women. Gilligan (1982, 1988) suggests women are more
likely to equate morality with caring for others (the ‘care perspective’) than men
who are more likely to equate morality with not infringing on others (the ‘justice
perspective’). This might suggest that women would cooperate more than men in
the experimental setting since free riding harms others but at the same time it is a
‘right’ of participants in these experiments. Kuhlman and Wimberley (1976) on
the other hand, contend that individuals typically demonstrate one of the following
three motives in the experimental setting: (a) individualistic
(chose to maximize
own gain) (b) competitive (chose to maximize gain relative to others) and (c)
cooperative (chose to maximize joint gain), and that men and women appear to be
equally represented in all three categories.
The evidence on gender differences in experimental economics is also mixed.
Marwell and Ames (1981) report significantly higher free riding behavior among
economics graduate students than other experimental subjects, a result confirmed
by Carter and Irons (1991). Rosenbluth, in a response to Carter and Irons, notes
that economics students are more likely to be male than the general population of
students and suggests that women ‘care more about what others think of them than
men do’ (Rosenbluth 1992, 202).
Mason et al. (1991) address the issue of gender differences in behavior in a
duopoly setting within a non-cooperative
repetitive game with anonymous opponents. They find that women start out more cooperative than men, but, after
repetition, men became more cooperative so that by the end of the experiment no
significant difference in the output choices of men and women were observed.
According to the authors, ‘one interpretation of this result is that market forces, in
the form of the profit motive, act to drive subject behavior regardless of the
subject’s initial predisposition’ (Mason et al. 1991, 232).
Rapoport and Chammah (1965) find significant differences in the behavior of
men and women in two-person repetitive games with a known opponent. All-male
pairs colluded 55% of the time, all-female pairs 33% of the time and mixed pairs
40% of the time. They suspect that this difference results from the greater
propensity of male pairs to play ‘tit-for-tat’ (rewarding the partner for a collusive
choice more quickly than female pairs did) thus enabling male pairs to reach the
cooperative solution sooner. Greater cooperative behavior by males was also found
by Brown-Kruse and Hummels (1993) in quadopoly experiments with all-or-nothing contributions.
C. Nowell, S. Tinkler / .I. of Economic Behavior & Org. 25 (1994) 25-36
27
It is currently unclear whether gender is an important determinant of choice. It
would appear that the size and direction of gender differences in subject behavior
might be sensitive to experimental design. For example, the anonymity of subjects
in the Mason et al. experiments may have been responsible for the lack of
evidence of gender differences in behavior since Eagly (1987) reports that people
behave in more gender stereotypical ways if they are identifiable by others.
We construct an experimental market using male and female subjects in which
group members can observe each other (in reality, economic transactions are
seldom anonymous) to see if this activates gender differences in behavior that
might be subdued in the Mason et al. (1991) experimental design.
In section 2, an experiment is described that attempts to uncover the role of
gender in determining contributions to a public good. Section 3 reports the results
of statistical analysis of data collected from this experiment, and conclusions are
found in Section 4.
2. Experimental
design
Undergraduate
subjects were recruited from introductory courses at Weber
State University during the academic year 1991-1992. A total of 64 subjects (30
men and 34 women) were divided into experimental groups of 4 subjects each.
Five of the groups were all-male, six were all-female, and five were mixed gender
(2 men and 2 women).
All subjects were volunteers who were told they would be participating in an
experiment about ‘how people make choices’. They were told at the time of
recruitment
that participants
could earn substantially
more than the ‘typical
student’s wage’ and that the experiment would last ‘about an hour’. (The
individual payoff varied between approximately
$9 and $16, with the average
earnings equal to $13.50, which included a $5.00 participation fee. The experiments lasted between 35 and 45 minutes.) Subjects were told that no special skills
were needed to participate in the experiment. None of the subjects had taken part
in decision making experiments prior to their enrollment in this study.
Once assembled for the experiment, subjects were given a printed set of
instructions which were read aloud (Appendix A). Subjects were told that any
communication
during the experiment would result in abandonment of the experiment and payment of a $5 participation fee only. Subjects had the opportunity to
ask questions regarding the instructions and did so in 2 of the 16 groups.
The experimental design is identical to that employed in experiments conducted
by Isaac and Walker (19881, except that we extend the experiment for three
additional periods. In the Isaac and Walker experiments,
the end period was
known with certainty while in our experiments, students knew the experiment
would not last for more than one hour, and could observe that sixteen periods were
listed on the chalk board. All subjects received an endowment of 62 tokens at the
28
C. Nowell, S. Tinkler/ J.
of Economic Behavior & Org. 25 (1994) 25-36
beginning of each time period to be divided between a private and
(GOOD A and GOOD B, respectively).
Investment in GOOD A
every token invested. Investment in GOOD B returned $.012 to
token invested, i.e. payment to each individual from investment
equalled:
(l/4)
a public good
paid $.Ol for
the group per
in GOOD B
1.q af,),
where Mi represents individual i’s contribution to GOOD B. GOOD B, therefore,
fits the strict definition of a public good in that it is non-excludable
and jointly
consumed.
At the beginning of each time period, subjects recorded their desired allocation
of tokens between GOOD A and GOOD B in a table (Appendix
B). The
experimenter added up total contributions to the public good by moving silently
between the subjects who were sitting apart from each other in a classroom. Total
investment by the group in the public good was recorded on a chalk board in a
column headed ‘Investment in GOOD B’. This figure was multiplied by 1.2 and
the result recorded in a column headed ‘Group Earnings from GOOD B’. Finally,
‘Group Earnings from GOOD B’ was divided by 4 and the result recorded as
‘Individual
Earnings from GOOD B’. This procedure was designed to make
concrete the relationship
between group investment
in the public good and
individual earnings from the public good.
Subjects calculated and recorded their earnings from GOOD A (number of
tokens invested X $.Ol), earnings from GOOD B (from the chalk board) and total
earnings at the end of each time period. Students were told that the experiment
would last for at least 10 trials. For each group, a total of 14 time periods were
completed (including a test period for which no earnings were paid and after
which the experimenter
checked to see that subjects had filled in their tables
correctly). Subjects could observe that space for 16 time periods had been marked
on the chalk board.
Although games such as the one described above contain a game theoretic
solution which prescribes non-cooperative
behavior, cooperation still appears to be
a common behavior of experimental subjects, particularly in the case of inexperienced subjects. If subjects do have an intended period of defection from the
cooperative outcome, as is argued by Selton and Stoecker (19861, the unexpected
end of the experiment may have helped reduce end-effect plays if the intended
period of defection was after period 14. Additionally,
Selton and Stoecker show
that defection from the cooperative outcome becomes more common as subjects
gain experience. Our subjects were completely inexperienced.
3. Experimental
results
Data on individual choices is summarized in Table 1 and further described in
Figure 1. We first note that, like Isaac and Walker (1988), we find significant
C. Nowell, S. Tinkler/J.
of Economic Behavior & Org. 25 (1994) 25-36
29
Table 1
Average
All-
choice of groups by period
T
1
2
3
4
5
6
7
8
9
10
11
12
29.4
28.6
22.5
20.4
23.4
20.4
23.2
21.2
17.2
18.7
11.0
12.1
11.2
9.1
29.2
31.3
26.9
27.7
27.1
26.1
25.4
26.7
22.2
19.2
18.8
17.1
14.4
18.3
27.6
28.0
24.1
20.7
18.6
19.8
14.9
23.0
20.5
13.5
10.4
8.8
16.9
14.3
13
Male
AllFem.
Mixed
levels of free riding for all individuals in all groups. Secondly, the extent of free
riding increased throughout the experiment. This is consistent with Isaac and
Walker, but in contrast to Mason et al. (1991) who find that in duopoly
experiments, subjects became more cooperative over time.
During the test period, the average contribution
to the public good of all
individuals who participated in the experiment was 26.9 tokens. In the first period
for which earnings were paid, the average contribution increased slightly to 27.8
tokens which is still only about 44% of total tokens available. During the last time
period the average contribution fell to 13.4, at which point less than 25% of total
tokens were invested in the public good.
We turn now to a comparison of the individual choices of the different groups.
Looking at Figure 1, it is clear that all-female groups tended to make higher
contributions than all-male or mixed gender groups. The contributions of all-female
groups were greater than that of all-male groups in every period except the
practice round, and greater than the mixed groups in all but one period. Casual
observation also suggests that the rate of deterioration of contributions
among
all-male groups was greater than that of the other groups. Comparing the average
individual’s
choice during the first 3 periods with that of the last 3 periods,
CHOICE
(tokens)
Test
1
2
3
4
5
6
7
8
9
10
11
12
L3
Period
-m-
Mm -(3-
women -+-
Fig. 1. Mean choice by period.
Mixed
Gender
30
C. Nowell, S. Tinkler/J.
of Economic Behavior & Org. 25 (1994) 25-36
all-male groups’ contributions
declined from 26.88 to 10.80 tokens or by 60%.
All-female groups’ contributions over this same time frame declined from 29.13 to
16.60 tokens, or by 43%. Mixed groups’ contributions to the public good declined
from 26.63 to 13.33 tokens, or by 50%.
Two issues of statistical specification arise in analyzing experiments such as
these. First, we consider the appropriate unit of analysis. During any period of the
experiment,
subjects independently
make choices based on a common set of
information. Each individual knows historical group choices but makes his or her
contribution to the public good as an individual. Second, our goal is to analyze the
variance of individual behavior across genders, but there are other possible sources
of the variation in individual choices including, importantly, variation across time
periods and variation between groups. We recognize that a correlation exists
between time periods in the F-tests and t-tests described below. In the regression
analysis described later in the paper, we use an autoregressive model to account
for this correlation.
In order to account for that portion of individual variation explained by group
membership as opposed to gender, we compare the variance of individual choices
within groups to the variance of group choices across the three gender categories.
If no significant differences exist, we can be confident that our final step of
comparing individual choices across gender is not overlooking a significant group
effect. The data break down into 3 gender categories, 16 groups, and 64 individuals. An F-test comparing the group mean square error across gender categories (16
group averages - 3 gender category averages = 13 degrees of freedom) to the
mean square error for individuals within groups ((4 individuals per group - 1
group average) . 16 groups = 48 degrees of freedom) indicates that no significant
differences exist (p-value > .75 for every period). Based on this test, group is
dropped from all further analysis, leaving the mean square error for individuals as
the appropriate error term for testing gender category effects.
We use an F-test to look for differences between the mean level of contributions (Ho: P,,,~,~ = pLfemale= pmixed) of the three gender categories. Results of the
analysis of variance test indicate significant differences at the 15% level for period
10 and at the 20% level for periods 6 and 11. This is certainly not strong evidence
that gender category is a significant determinant of differences in the level of
public good provision.
Table 2 focuses on the difference between all-male and all-female groups. This
table shows the average difference between all-male groups’ and all-female
Table 2
Differences
d!
t,
in mean contribution
bv ueriod (all-female-all-male)
T
1
2
3
4
5
6
7
8
9
10
I1
12
13
- 0.2
-0.07
2.7
0.41
4.4
0.78
7.3
1.43
3.1
0.65
5.7
1.15
2.2
0.40
5.5
0.93
5.0
0.88
0.5
0.00
7.8
1.66
5.0
1.16
3.2
0.61
9.2
1.87
Notes: ‘d, = average contribution
all-female
groups-
average contribution
all-male groups.
C. Nowell, S. Tinkler/J.
of Economic Behavior & Org. 25 (1994) 25-36
31
groups’ choices for each period and the associated t-statistic calculated as t = (X,
- X,)/S(l/n,
+ l/n,).
S is the (weighted) estimated standard deviation of the
difference between the sample means, and X, and X, are the mean contributions
of nf women in all-female groups and nm men in all-male groups. Differences are
relatively constant throughout the experiment. Even though men consistently
contributed less than women, the difference is significant (at the 10% level) in
periods 10 and 13 only.
Tables 1 and 2, and Figure 1 present inconclusive
evidence of the effect of
gender categories on contributions
to the public good. We further explore a
possible relationship between gender categories and contributions
to the public
good using regression analysis. The structure of the model employed here is
similar to that of Mason et al. (1991). The behavioral model we begin with rests
on the simple assumption that an individual’s
choice of how many tokens to
contribute to the public good in period t, (C,), is determined by an autoregressive
process described by the following equation:
Ci, = (Y+ B,d, + I&d,,
+ I&G,,_ 1 + qt,
(1)
where (Y is a constant term, Gi,+ 1 is his or her entire group contribution
prior period, d, is a dummy variable equal to one if the individual is
all-female group, zero otherwise and d,, is a dummy variable equal to one
individual is in a mixed group, zero otherwise. lit, an error term, follows
order autoregressive process described by:
lit = pi Eit- 1 + vi, 7
in the
in an
if the
a first
(2)
where Vi, is normally distributed. Our model is completed by using equation (1) to
characterize eit and lit_ ,; substituting these expressions into equation (2), and
solving for Ci,.
We estimate the following equation using 768 observations:
Ci, = (Y( 1 - p) + a,d,(
- phxGit-2 + Vit,
1 - p) f B,d,o(
1 - p) + pCi,_ 1 + 133Gi,_ 1
(3)
where the parameter I3, represents the individual’s reaction to changes in group
contributions, and the coefficient p represents the influence of an individual’s past
choice on their current choice.
Running one regression for the entire data base is appropriate if no heterogeneities between the groups exist. Prior to aggregating the three groups into one
data set, we analyzed the data for each group separately and obtained estimates for
both p and the standard error of each regression. An F-test was used to compare
the sum squares of the restricted model with the sum squares of the three separate
models. We reject the hypothesis that the serial correlation coefficient is different
between groups. Apparently the reaction of the individual towards the group
contribution in the prior period is not dependent on group type. In addition, no
significant differences were found when comparing the standard errors individu-
32
C. Nowell, S. Tinkler/J.
of Economic Behavior & Org. 25 (1994) 25-36
ally estimated for the three groups. Thus, no significant heterogeneities exist in the
data.
In equilibrium, an individual’s choice will remain constant over many periods,
thus CT = Ci, = Ci,_ 1, and Gi,_ i = Gi,_ 2 = 4CT. Making these substitutions into
equation (31, and solving for CT yields the equilibrium choice for each group
type:
C*, = a/(
1 - 48,)
C*, = ( (Y+ l3,)/(
for all-male groups,
1 - 48,)
and C*,, = ( (Y+ a,)/(
for all-female
1 - 48,)
groups,
for mixed gender groups.
(4)
In this formulation, we allow for different equilibrium levels of contribution for
each group, but restrict the dynamic interaction of all three groups to be identical.
The estimated coefficients 0, and 13, are used to calculate the difference in
equilibrium choices between all-male, all-female and mixed groups.
Because of the non-linearity
of equation (3), we use a nonlinear least squares
procedure to minimize:
{Cit- [(11(1-P>
+gidr(l-P)
+g~dl~~o(l-P)
‘PCit+i
f gaGit_i
(5)
A Newton-Raphson
algorithm was used to estimate CY,l3,, B,, I&, and p.
Convergence was achieved after ten to fifteen iterations depending on the starting
values. Our results do not appear to be sensitive to the starting values chosen.
Results of the procedure are presented in Table 3.
The autoregressive nature of individual contributions appears to be confirmed,
as the estimated coefficient p is positive and significant. The estimated coefficient
13, is negative but insignificant.
The negative sign would seem to indicate that
individuals in the group may try to counteract the behavior of the group as a
whole, although with a t-statistic of - 0.50, this effect is probably not important. It
would appear that subjects are influenced by their own prior behavior, not the
behavior of other members of the group.
Table 3
Regression
results
Coefficient
Estimated
Value
Asymptotic
t-statistic
,*I
16.19
5.82
0.21
- 0.01
0.56
5.92
1.83
0.06
- 0.50
17.45
a2
R,
P
n = 768
F = 92.5
C. Nowell, S. Tinkler / J. of Economic Behavior & Org. 25 (1994) 25-36
33
An alternative specification would be replace Gi, _ 1 with the sum of all other
group members’ contributions (Gi,_ 1 - Ci,_ I). Using this specification, we found
that the likelihood function, as well as estimated values and significance levels for
cy, I.$ and p remain virtually unchanged. The significance of 13, increases and that
of I3, decreases. The effect of this change on our conclusions relating to gender are
negligible and we drop this specification from further consideration.
The estimated coefficient l3, is positive and significant at the 10% level in a
two-tailed test with a t-statistic of 1.83. It appears that the equilibrium contribution
of individuals in all-female groups may be different from the equilibrium contribution of individuals in all-male groups. The same cannot be said for the equilibrium
contribution
in mixed groups, as the estimated coefficient l3, is insignificant.
Equilibrium contributions of all-male, all-female, and mixed groups are calculated
using equation (4); and are 15.56, 21.16, and 15.76 respectively.
4. Conclusion
Our work suggests that all-female groups may be more cooperative than
all-male groups in public goods experiments and that this difference does not
diminish over time. We provide some evidence that in equilibrium, the ultimate
contribution
of all-female groups is likely to be greater than that of all-male
groups. Additionally,
women would appear to be more influenced by men than
vice versa since in our experiment mixed gender groups contribute very close to
the equilibrium contribution of all-male groups (which supports Eagly (1987) who
finds women more ‘influenceable’
than men). The results that all-female groups
may be more cooperative than all-male groups is at odds with work by Rapoport
and Chammah (1965) and Brown-Kruse
and Hummels (1993), who both find
women less cooperative, and Mason et al. (19911, who find no difference between
men and women.
These seemingly contradictory results can likely be explained by experimental
design. Both Rapoport and Chammah and Mason et al. conducted duopoly
experiments,
the former with known rivals, the later with an unknown rival.
Gender differences in behavior that may be subdued in the Mason et al. experiments may be activated simply by the knowledge of the gender makeup of the
group. In addition, defection from the cooperative outcome is more likely in
quadopoly experiments (such as ours) than duopoly experiments because it is
possible to escape detection by other group members.
Brown-Kruse and Hummels conducted quadopoly experiments, as we did, but
significantly their subjects were required to make ‘all or nothing’ contributions to
the public good, whereas we permitted subjects to partially defect from the
cooperative solution by allowing contributions from 0 to 64 tokens. Men may be
more likely to cheat than women when the experimental design is such that the
possibility of detection is reduced.
34
C. Nowell, S. Tinkler/ J.
of Economic Behavior & Org. 25 (1994) 25-36
Since gender differences would seem to be more forcefully expressed in
environments
in which the gender of the other subjects is known, they might be
even more strongly expressed in experiments designed to allow for communication
between ‘rounds’. Men and women have different communication
styles and view
the role of conversation differently (Tannen 1990). Therefore, since an environment that permits communication
might be regarded as more ‘realistic’, it might
be informative to examine the role of gender on contributions in an experimental
framework that permits communication.
What are the possible implications of this finding of greater cooperation among
all-female groups than all-male or mixed groups? A commonly observed practice
in organizations today is for women to be added to committees, work-teams and
other groups in the hopes of getting more diverse opinions and changing the
outcomes of committee processes. Our experiments suggest that this strategy may
not work since the outcomes of mixed groups and all-male groups are very similar
and if a unique ‘female perspective’ is desired it may only be obtainable by
forming all-female groups.
Appendix
A. Experimental
instructions
You are about to participate
The purpose of this experiment
processes. If you pay attention
considerable amount of money.
of the experiment.
in an experiment about economic decision making.
is to gain insight into certain features of economic
and follow the instructions carefully you can earn a
All earnings will be paid to you in cash at the end
1. Background
You are one person in a group of four. Any form of communication
between
members of the group is forbidden.
Each member of the group will be given tokens which they can invest. In order
to earn money you must invest the tokens. You can invest the tokens in GOOD A
or GOOD B. Each member of the group will be given 62 tokens. You can divide
these tokens between the two goods in whatever manner you wish.
2. The payoff
GOOD A
For every token you invest in GOOD A you will receive 1 cent in return.
If you invest 62 tokens in GOOD A you will receive $.62 (62 cents).
C. Nowell, S. Tinkler /J. of Economic Behavior & Org. 25 (1994) 25-36
35
GOOD B
The payoff for investing in GOOD B is more complicated. For every token that
you or any other member of the group invests in GOOD B the group will receive
1.2 cents in return. The group will divide the 1.2 cents equally between its
members, thus you will receive 3 cents for every token the group invests in GOOD
B.
If you or any other member of the group invests 62 tokens in GOOD B, then
every member of the group will receive $0.186 (18.6 cents).
The actual experiment
will proceed as follows:
1. You and the other members of the group will privately and independently
select the number of tokens you wish to invest in GOOD A and GOOD B. Record
this on the RECORD SHEET in front of you.
2. One of the experimenters will look at the record sheets and write the total
group investment in GOOD B on the chalkboard.
3. Record on the record sheet your earnings from GOOD A and GOOD B.
Remember your earnings for GOOD B are equal to one-fourth of the group
earnings. Your earnings from GOOD A are equal to 1 penny for each token
invested in GOOD A.
4. Calculate your total earnings by adding your earnings from GOOD A and
GOOD B. Record this amount on the record sheet.
5. The experiment will continue for at least 11 trials. The first trial will be a
practice trial. On the record sheet this trial is called Pl.
6. Your total earnings will be the sum of what you earn in the trials (excluding
the practice trial) plus a $5.00 participation fee. Your earnings will be paid to you
in cash at the end of the experiment.
Appendix
B. Student record sheet
Record sheet
Pl
Tl
T2
T3
Investment
in Good A
Investment
in Good B
Earnings
Good A
Earnings
Good B
Total
Earnings
Each period you invest 62 tokens
T4
T5
T6
T7
T8
T9
TlO
Tll
T12
T13
T14
T15
36
C. Nowell, S. Tinkler / J. of Economic Behavior & Org. 25 (1994) 25-36
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