K.M. Brown, L.O. Taylor J. of Economic Behavior Org. 43 2000 127–139 131
Conservancy; those who state a zero value are told to throw away the payment form and en- velope in the privacy of their own home. Once the Nature Conservancy receives a check, they
verify that the amount on the check matches the amount written on the payment form and then mails the payment form back to Georgia State University so that it can be matched by iden-
tification number to the subject’s questionnaire subjects are also told this information.
8
The hypothetical treatment consists of an identical description of the payment mecha- nism with the exception that subjunctive language is used and subjects are not provided with
payment forms or envelopes. In addition, subjects are reminded several times in the hypo- thetical treatment that they are participating in a hypothetical survey and are not actually
being given the opportunity to send money to the Nature Conservancy.
This experimental design allows us to test several hypotheses related to gender. First, we test for gender differences in stated values in the hypothetical treatment and then repeat this
test for values elicited in the real treatment. These comparisons allow us to examine the preferences of females versus males for the public good offered in these experiments. While
we have no expectations as to whether females or males might report higher values for this good, ceteris paribus, we do expect the results to be consistent across treatments if there are
no behavioral effects due to the valuation mechanism. In other words, if males state higher WTP than females in the hypothetical treatment, then we might also expect males to state
higher WTP than females in the real treatment. Second, and related to the previous tests, we conduct out-of-sample tests to examine whether or not hypothetical bias exists for females
and males and whether or not it is differentiated according to gender. Following Gilligan, and the interpretation of her work by Cadsby and Maynes, we might expect hypothetical
bias to be smaller for females than for males if females are more likely to respond to the market context.
3. Empirical results
Surveys are conducted with 488 subjects.
9
WTP responses and several relevant summary statistics are presented in Table 1 by treatment and gender. As indicated in Table 1, there
8
It is important to note that this design essentially requires subjects in the real treatment to pledge a contribution during the experiment and then send an actual payment once they leave the experiment. This design serves two
important purposes. First, it allows as much anonymity as possible. Other on-the-spot payment mechanisms would reveal who stated a positive value and who did not, which could invite peer-pressure effects. Second, this payment
mechanism does not require subjects to have cash or checks available at the time of the survey, which is important since they would not have anticipated the need for these items. Results show that 52 percent of subjects who stated
a positive value in the real treatment mailed in their contribution — thus, stated values in the real treatment were different than actual payments. In our analysis, we treat stated values in the real treatment as equivalent to actual
values had payments been binding say, had we employed follow-up requests. Our overall conclusions do not change if we include the “follow-up” behavior as part of the analysis as discussed in Footnote 14. Therefore, for
clarity and succinctness we do not focus on this aspect of the experimental design.
9
Data are pooled from 246 adults and 242 students. The student body at Georgia State University is comprised of many non-traditional students. The average age of the student sample is 26 with a range 20–51 and the average
household income is 52 141 with a range 2500–125 000. We find it reasonable to pool the data as Brown 1999 finds no evidence of significant differences in values across these groups once income and other demographic
differences are controlled for in the regression analysis. However, we also control for student status in the analysis.
132 K.M. Brown, L.O. Taylor J. of Economic Behavior Org. 43 2000 127–139
Table 1 Descriptive statistics
Variable Hypothetical treatment
a
Real treatment
a
Female Male
Female Male
Stating a positive WTP 63.76
64.95 22.46
28.85 Mean willingness to pay
27.97 72.22
3.23 6.14
52.75 163.82
7.66 13.37
[0–500] [0–1000]
[0–50] [0–50]
Household income
b
×10
3
59.64 70.68
48.75 49.06
38.74 37.31
32.22 34.35
[2.5–125] [2.50–125]
[2.5–125] [2.5–125]
AGE 33.21
42.10 35.90
38.29 14.37
16.60 12.76
14.30 [20–77]
[20–81] [20–68]
[21–84] N
149 97
138 104
a
Standard deviations are in parentheses and the range of values are in brackets.
b
Income is based on the mid-point of responses to an interval question asking the annual pre-tax income. The intervals are 5000 or less, 5001–15 000, 15 001–30 000, 30 001–45 000, 45 001–60 000, 60 001–75 000,
75 001–90 001, 90 001–100 000, and over 100 001.
are 149 females and 97 males in the hypothetical treatment and 138 females and 104 males in the real treatment. There is no significant difference in the percentage of females and
males stating a positive value in both the hypothetical treatment approximately 64 percent and the real treatment approximately 25 percent.
10
However, the mean willingness to pay for females is 27.97, while the mean willingness to pay for males is 72.22, in the
hypothetical treatment, and these differences are significant t=2.57. Similarly, in the real treatment, the mean willingness to pay for females is 3.23 and the mean willingness to
pay for males is 6.14 and these are just significantly different at the 95 percent level of confidence t=1.99. Although the “raw” mean willingness to pay responses suggest that
males state higher values in both hypothetical and real treatments — suggesting that males may have stronger preferences for the public good than females — these results also suggest
that hypothetical bias may be stronger for males than for females. To test this hypothesis more formally, we next present models estimating WTP responses while controlling for
other factors such as income that may influence behavior.
The data are characterized by a “spike” at zero and a right-skewed distribution, therefore the normal distribution is likely to be inappropriate for our estimation models. Because
alternative distributions, such as the Gamma, log-normal, and Weibull, are only supported in the positive quadrant, we employ the hurdle model see, e.g., Gurmu, 1997; Brown
et al., 1999. The hurdle model handles a non-negligible portion of zero responses and a skewed distribution in the data by maximizing a likelihood function that estimates the
probability of a spike at zero as well as the factors impacting only the positive responses.
10
t -Statistics testing the null hypothesis of no significant difference in the percent stating a positive value across
gender are t=0.19 and 1.13, for the hypothetical and real treatments, respectively.
K.M. Brown, L.O. Taylor J. of Economic Behavior Org. 43 2000 127–139 133
Similar to the Tobit model, the hurdle model is a mixture of discrete and continuous parts. The discrete component of the hurdle model estimates the probability that a subject will
state a positive value called the “participation decision” as a function of attitudes and demographic characteristics; the continuous component of the hurdle model is estimated for
only those subjects stating a positive value called the “contribution decision” as a function of attitudes and demographic characteristics.
11
The participation decision is estimated with a probit model and the contribution decision is estimated by maximum likelihood, assuming
a log-normal distribution.
12
Table 2 presents the results of hurdle models estimating the factors that influence the participation and contribution decisions in a pooled model i.e., the full sample pooled
across females and males, as well as hypothetical and real treatments and models with only the observations in the hypothetical treatment and the real treatment, separately. In
addition to the coefficient estimates, Table 2 presents the marginal effects for the gender, treatment, and income variables. The models control for gender GENDER=1 if male and
GENDER=0 if female, as well as the following demographic and attitudinal variables:
REAL = 1 if treatment is a real survey,
0 if hypothetical, ADULT =
1 if subject is not recruited through a University group, 0 otherwise,
AGE = the age of the subject, EMPLOY =
1 if subject is employed full-time, 0 otherwise,
HHINCOME = household income see Table 1, footnote b for a complete definition, BUDGET =
1 if subject is primarily in control of the household budget, 0 otherwise,
RACE = 1 if subject is Caucasian, not of Hispanic decent,
0 otherwise, MARRIED =
1 if subject is married, 0 otherwise,
EDUC = 1 if subject has a college degree,
0 otherwise,
11
Gurmu 1997 demonstrates that estimating these two parts of the hurdle model i.e., maximizing separate likelihood functions is equivalent to the maximization of the joint likelihood function for both the discrete and
continuous components.
12
The log-normal distribution is preferred to the Gamma and Weibull distributions based on the value of the log-likelihood; the value of the log-likelihood is maximized in all cases when we assume a log-normal distribution.
134 K.M. Brown, L.O. Taylor J. of Economic Behavior Org. 43 2000 127–139
RANK =
1 if subject characterizes the Adopt an Acre program as very unimportant to the goal of saving rainforests,
2 if moderately unimportant, 3 if moderately important,
4 if very important,
RATE =
1 if subject rates the Adopt an Acre program as much less favorable to other programs he or she might support,
2 if less favorable, 3 if about the same,
4 if moderately favorable, 5 if much more favorable,
AWARE = 1 if the subject was previously aware of the Adopt an Acre program,
0 otherwise. Results for the pooled model indicate that gender is not a significant predictor of the
participation decision column 1a, but is a significant predictor of the contribution decision column 1b, after controlling for treatment, attitudes, and other demographic characteristics
of the subjects. In other words, although females and males choose to contribute at the same rate the participation decision, once they decide to contribute, males state higher values
than females the contribution decision. Specifically, of those who decide to contribute to the Nature Conservancy, males state values that are 13.34 higher than females, according
to the marginal effects. This model also indicates that being in the real treatment REAL reduces the probability that a subject states a positive value by almost 50 percent see column
1a, and of those who state a positive value, being in the real treatment reduces WTP almost 40 as compared to those in the hypothetical treatment. Attitudes towards the Adopt an
Acre program RANK and the Nature Conservancy RATE are significant predictors of the participation decision, while demographic factors such as income, marital status, and
gender are significant predictors of the contribution decision.
While the pooled model indicates that gender is a significant predictor of behavior after controlling for treatment, this model restricts gender effects to be linearly related. To relax
this assumption, we also report hurdle models estimated for the hypothetical treatment separately from the real treatment in columns 2a, b and 3a, b of Table 2, respectively.
These models indicate that gender is not a significant predictor of the participation decision in either the hypothetical or real treatment see columns 2a and 3a, just as suggested by
the model pooled across treatments. However, when considering the contribution decision for those who state a positive value, males state statistically higher values than females in
the hypothetical treatment column 2b, but not in the real treatment column 3b.
13
In the hypothetical treatment, males state values that are 28 higher, on average, than females.
13
Similarly to the pooled model, other variables that are significant predictors of behavior vary depending on the treatment, and whether one is considering the participation decision 2a and 3a or the contribution decisions 2b
and 3b.
K.M. Brown, L.O. Taylor J. of Economic Behavior Org. 43 2000 127–139 135
Table 2 Regression results
a
Variable Pooled model
Hypothetical model Real model
1a Partici- pation
decision 1b Contri-
bution decision
2a Partici- pation
decision 2b Contri-
bution decision
3a Partici- pation
decision 3b Contri-
bution decision
Intercept −
2.59
∗∗∗
1.77
∗∗∗
− 3.57
∗∗∗
1.44
∗∗
− 2.78
∗∗∗
1.88
∗
0.46 0.56
0.67 0.68
0.77 1.01
GENDER 0.12
0.32
∗∗
0.07 0.50
∗∗
0.13 −
0.08 0.14
0.16 0.22
0.21 0.20
0.24 [0.049]
[13.34] [0.026]
[27.54] [0.39]
[1.34] REAL
− 1.21
∗∗∗
− 0.95
∗∗∗
0.14 0.17
[−0.478] [−38.98]
ADULT 0.19
0.06 0.68
0.42 −
0.05 −
0.22 0.24
0.24 0.43
0.35 0.31
0.31 AGE
− 0.008
− 0.002
− 0.01
− 0.009
− 0.005
0.004 0.007
0.008 0.01
0.009 0.011
0.013 EMPLOY
0.29 0.29
− 0.08
− 0.15
0.45
∗
0.84
∗∗∗
0.19 0.20
0.32 0.27
0.25 0.28
HH INCOME 0.002
0.005
∗∗
0.006
∗∗
0.006
∗∗
− 0.005
0.002 0.002
0.002 0.003
0.003 0.003
0.006 [0.20]
[0.31] [0.03]
BUDGET −
0.002 −
0.07 −
0.17 0.04
0.04 −
0.33 0.17
0.19 0.25
0.23 0.25
0.35 RACE
0.08 0.09
0.22 0.02
0.01 0.25
0.17 0.19
0.27 0.27
0.22 0.27
MARRIED 0.06
0.39
∗∗
0.11 0.36
∗
0.09 0.57
∗∗
0.16 0.17
0.24 0.22
0.23 0.29
EDUC −
0.24 0.01
− 0.43
∗
0.14 −
0.03 −
0.25 0.16
0.18 0.25
0.22 0.21
0.27 RANK
0.52
∗∗∗
0.16 0.53
∗∗∗
0.33
∗∗
0.47
∗∗∗
− 0.20
0.11 0.14
0.15 0.16
0.18 0.24
RATE 0.40
∗∗∗
0.14 0.69
∗∗∗
0.07 0.17
0.24 0.08
0.09 0.14
0.11 0.12
0.15 AWARE
0.18 −
0.13 −
0.23 −
0.02 0.55
∗∗
− 0.24
0.17 0.17
0.25 0.22
0.24 0.29
Scale 1.01
∗∗∗
1.02
∗∗∗
0.85
∗∗∗
0.05 0.06
0.08 L
− 239.52
− 300.87
− 112.42
− 218.91
− 114.65
− 73.81
N 461
211 237
152 224
59
a
In each model the participation decision is a probit model where the dependent variable is equal to one if the subject states a positive value and 0 otherwise, and the contribution model is a maximum likelihood model for
those who state a positive value, assuming a log-normal error distribution. Standard errors are in parentheses and marginal effects are reported in brackets, for select variables. Marginal effects are evaluated at the mean of the
independent variables.
∗
90 percent level of significance.
∗∗
95 percent level of significance.
∗∗∗
99 percent level of significance.
136 K.M. Brown, L.O. Taylor J. of Economic Behavior Org. 43 2000 127–139
Table 3 Regression results by gender
a
Variable Females only
Males only 1a Participation
1b Contribution 2a Participation
2b Contribution decision
decision Decision
decision Intercept
− 2.54
∗∗∗
1.55
∗∗
− 2.67
∗∗∗
2.69
∗∗∗
0.62 0.64
0.73 0.96
REAL −
1.28
∗∗∗
− 0.68
∗∗∗
− 1.15
∗∗∗
− 1.22
∗∗∗
0.19 0.20
0.23 0.29
[−0.50] [−20.36]
[−0.51] [−69.00]
ADULT −
0.07 −
0.02 0.30
− 0.04
0.32 0.29
0.38 0.39
AGE −
0.012 0.019
∗∗
0.0004 −
0.014 0.010
0.009 0.010
0.011 EMPLOY
0.09 −
0.14 0.58
∗∗
0.61
∗∗
0.27 0.26
0.29 0.30
HH INCOME 0.003
0.005
∗
0.0002 0.004
0.003 0.003
0.003 0.004
[0.15] [0.25]
BUDGET 0.10
0.22 −
0.16 −
0.40 0.23
0.22 0.27
0.32 RACE
− 0.04
0.37 0.15
0.12 0.23
0.26 0.25
0.29 MARRIED
0.23 0.37
∗
− 0.30
0.26 0.22
0.20 0.26
0.29 EDUC
− 0.15
− 0.15
− 0.26
0.20 0.21
0.21 0.24
0.29 RANK
0.52
∗∗∗
0.13 0.54
∗∗∗
0.15 0.15
0.16 0.16
0.22 RATE
0.42
∗∗∗
− 0.03
0.36
∗∗∗
0.15 0.11
0.11 0.14
0.15 AWARE
0.25 −
0.26 0.01
− 0.12
0.22 0.20
0.27 0.29
Scale 0.86
∗∗∗
1.08
∗∗∗
0.05 0.08
L −
138.36 −
154.26 −
97.49 −
133.14 N
269 122
194 89
a
Participation and contribution decisions are described in footnote a of Table 2. Standard errors are in paren- theses and marginal effects for selected variables are reported in brackets. Marginal effects are evaluated at the
mean of the independent variables.
∗
90 percent level of significance.
∗∗
95 percent level of significance.
∗∗∗
99 percent level of significance.
K.M. Brown, L.O. Taylor J. of Economic Behavior Org. 43 2000 127–139 137
However, in the real treatment gender is not a significant predictor of either the participation or contribution decision columns 3a and 3b.
14
These results indicate that females and males respond to the real treatment in a similar manner, suggesting similar preferences for the good, after controlling for demographic and
attitudinal variables. However, this is not the case for the females and males participating in the hypothetical treatment. There are two possible explanations for this result. First,
the sample of males in the hypothetical treatment may have had stronger preferences for the public good after controlling for demographic and attitudinal variables. Alternatively,
the males may have responded to the hypothetical treatment differently, in a behavioral sense, than females. We find the first explanation less plausible, given the results of the real
treatment in which there is no evidence of differences in preferences for the public good. We examine the second possibility next gender-related behavioral differences in response
to hypothetical treatments.
Table 3 presents hurdle models with subjects from both the hypothetical and real treat- ments disaggregated by gender. Results indicate that being in a real treatment REAL is a
significant predictor of behavior for both females and males, and in both the participation and contribution decisions.
15
The marginal effect of being in the real treatment for the participation decision reduces the probability of a positive value by 50 percent for both
females and males see 1a and 2a. Similar to the models reported in Table 2, gender does not appear to affect the rate at which subjects choose to contribute to the good. However, as
columns 1b and 2b indicate, being in a real treatment reduces WTP by 20, on average, for females and 69, on average, for males. Thus, after controlling for demographic and attitu-
dinal differences across gender, our models provide evidence supporting the “raw data” that hypothetical bias for the males in our sample is larger than for the females in our sample.
4. Conclusions
