2014 International Conference on Management Science & Engineering (21th)
August 17-19, 2014
Helsinki, Finland
A Behavioral Study on the Value of Elasticity
of Marginal Utility in Environmental Risks
XIE Charlene 1，LIU Yang1，SHE Sheng-xiang2
1 Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, P.R. China
2 School of Management, Guilin University of Technology, Guilin 541004, P.R. China
Abstract: The choice of elasticity of marginal utility
greatly affects time discount rate, and is thus key
parameter in welfare analysis across generations. This
research elicits the value of elasticity of marginal utility
with a behavioral experiment. Participants make
behavioral decisions under environmental risks the
experiment. Through the use of iso-elastic utility
function, we derive elasticity of marginal utility. We find
that the value of elasticity of marginal utility much lower
than those used in existing literature. In addition, we
notice that and people tend to overestimate the subjective
probability of environmental risks in the experiment. A
lower value of elasticity of marginal utility based upon
real environmental behavior suggests a lower time
discount rate. This is more preferable to make ethically
motivated decisions on the welfare distribution across
generations, and is more consistent with public attitudes.
Keywords: discount rate, elasticity of marginal
utility, environmental risk, intergenerational equity,
willingness to pay
1 Introduction
Economists have also analyzed environmental
problems with their unique tools. One important question
that they have paid much attention to is the distribution
of environmental welfare across generations. Our
offspring inherit their environment from us. How we
exploit environment directly affect their welfare [1]. So,
we have a responsibility to our offspring to pass on a
good environment to them. Yet, every generation tries to
maximize its own welfare. This calls for the tradeoff in
welfare between generations. This has been a key topic
in economic for a long time.
The publication of Stern Review in has rekindled
the hot academic debate on discount rate [2-3]. This is
largely due to the central role of discount rate in climate
policy and policies for other environmental problems.
Supported by the National Natural Science Foundation of
China (71371060, 71361004), the Humanities and Social
Sciences of Education Ministry (12YJA880130) and the Project
of Humanities and Social Sciences in Colleges of Guangxi
(SK13ZD021)
978-1-4799-5376-9/14/$31.00 ©2014 IEEE
Stern’s deal with climate change policy was based upon
Ramsey equation and the rejection of pure utility time
discount [4]. This approach tries to maximize welfare over
time with the choice of proper discount rate.
Ramsey equation is the most widely accepted
discount rate model:
(1)
ρ = δ + ηg
where ρ is the discount rate, δ is pure time discount
rate, g is is consumption growth rate, and η is the
elasticity of marginal utility [5]. While g relies on the
resource accumulation and technological progress of
and η are value judgments [6].
economy,
It is crystal clear that the choice of the value of
elasticity of marginal utility directly decides discount
rate. It is a measure of social preference for equality of
consumption among generations [7]. A high value of
elasticity of marginal utility suggests more current
consumption, while a low value of it underweights
current generation’s welfare [8]. Stern focused on the
elasticity of marginal utility in his discussion of
intergenerational welfare [2]. He assumed a value of 1 for
elasticity of marginal utility. But other researchers
disagree with this assumption; they have either assumed
or empirically found different values, as shown in Tab.1.
Tab.1 Estimated values of
Researcher
Blundell [10]
Dasgupta [11]
Cowell and Gardiner [12]
Evans [13]
Arrow et al. [7]
Weitzman [6]
Stern [1]
Nordhaus [2]
Garnaut [14]
value
0.83
>=2
1.28 / 1.41
1.4
2-4
2
1
2
1 and 2
It can be found from Tab.1 that the value of
elasticity of marginal utility varies much in different
studies. The highest estimation reaches 4, while the
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lowest value is only 0.83. Taking it into account that
elasticity of marginal utility is the curvature of utility,
such a divergence then implies a lack of corroboration in
both the willingness to pay for transforming risky
income into a certain income and the reallocation for
increased total utility [9].
In addition to divergence in estimation, there are
several problems with the value of elasticity of marginal
utility in existing studies. Three of them are extremely
important from technical aspects. The first problem goes
with the source of value. Despite the fact that debates on
social discount rate and discount utilitarianism center on
environmental issues, most existing studies estimate the
value of elasticity of marginal utility from situations
unrelated to environment. These include lifetime
consumption behavior [10], insurance decisions [11], and
income tax [13-14]. Those results derived from economic
behavior have nothing to do with environmental risk
perception and cognition [15]. The second problem goes
with the deal with risk. Although there is much risk with
environmental problem [16], few studies have estimated
elasticity of marginal utility with consideration of risk.
The third problem is about the domain of these studies.
Existing literature mainly focus on contingent gains.
However, environmental problems cause losses in most
cases [17].
The current study tries to estimate the value of
elasticity of marginal utility with people’s behavior under
environment risks. To our knowledge, this is the first
study that both focuses on environmental behaviors and
takes into account loss risks. The remaining parts of this
paper are arranged as follows. Section 2 discusses the
methodology and experimental design of our study.
Section 3 presents the results of statistical analyses.
Section 4 concludes with a brief summary and then
focuses on the need for further work and analysis.
2 Methodology
The discussion of discount rate of environment and
environmental goods should be situated environmental
context. Also, it should address the risk inherent in
environment. Out of these considerations, we design a
special experiment in which subjects face many
environmental risks that will harm their health if
realized.
2.1 Design
The specific background of the experiment is the
water pollution risks in China. Real-world environmental
risks are very uncertain and complex. However, risk
scenarios can be simplified with certain probability and
severity [18]. Six risk scenarios of water pollution risks
are designed which differ in outcome. Tab.2 shows the
risk scenarios used for this research.
xi represents the first possible outcome of
environmental risk situation i, yi is the second possible
outcome, and pi is the probability of xi. Taking the third
scenario as an example, its x is 1500, this means that if
the first outcome is realized, the subject will suffer a
health loss of 1500RMB; the probability p being 2/6, this
means that the probability of first outcome 1500 is 2/6;
its y is 750, meaning that when the second outcome is
realized, the subject will suffer a health loss of 750RMB.
This framing of environmental risks as health risks is
consistent with the finding of Maibach et al. (2010) [19].
Scenario
xi
pi
yi
Tab.2 Environmental risk scenarios
1
2
3
4
5
1500
2/6
0
750
2/6
0
1500
2/6
750
750
2/6
375
1250
2/6
500
6
1500
2/6
1125
Subjects are asked to choose the willingness to pay.
Willingness to pay has been widely used to show
people’s health risk perception [20]. In our study, we
define willingness-to-pay as the maximum value that
people are willing to pay to avoid the exposure to these
risks. Through the value of willingness to pay, we
quantitatively measure people’s felt utility of a particular
environmental risk. To accurately induce people’s
willingness to pay for environmental risks, we use
bi-section method in our study. The advantage of this
method lies in that it can gradually approaches to the
exact value prefigured in people’s mind. Subjects receive
a virtual account with 1500 RMB inside at the beginning
of the experiment. They choose among three options, “I
prefer to accept the risk”, “I prefer the certain loss”, and
“I feel indifferent between the risk and the certain loss”.
Should a subject chooses one of the first two options, the
certain loss displayed on the screen will adjust
accordingly until he or she chooses the third option. Then
the next environmental risk situation will be displayed.
The induced indifferent value is treated as the willing to
pay. This design is the same to that of Liu et al. (2014)
[21]
.
2.2 Procedure
Given its explorative nature, student sample is used
for this research. Student sample is commonly used in
risk perception studies [22-23]. In all, 75 students from
Harbin Institute of Technology Shenzhen Graduate
School were recruited. The size of student sample is 75,
and their ages ranged from 22 to 30 years (mean=24.2,
SD=1.44). 43 of them were female, and 32 (48 percent)
were male. This sample size can well serve the purpose
of this tentative research, meeting the minimum
requirement of relevant statistical analyses to be used.
Students were recruited on campus. They were
distributed with instructions about the experiment at least
two days in advance. This was to ensure that they could
well understand the requirements and procedures of the
experiment. Besides, we gave further oral instructions on
the day to ensure the efficacy of the experiment. In
addition, there was a warm-up section in the experiment,
in which subjects faced questions and choices of the
same style with those in the formal section. This made
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subjects familiar with the experiment and reduced the
biases caused by unfamiliarity.
Risk
1
2
3
4
5
6
2.3 Model
According to prospect theory [24], people evaluate a
risky situation with two possible outcomes via both
utility and subjective probability, i.e.
v( a, p; b, q ) = ω ( p )u (a ) + ω (q )u (b)
(2)
where a and b are the two possible outcomes, p and
q are the respective probability of a and b, w(p) and w(q)
are the subjective probability of p and q, u(a) and u(b)
are the utility of a and b. Thus, subjects in our
experiment are supposed to evaluate environmental risks
caused by water pollution according to the following
formula:
ω ( p )u (a ) + (1 − ω ( p))u (b)
a 1−η
1 −η
u (a) =
(4)
Using willingness to pay for these environmental
risk situations, we can simultaneously estimate the value
of w(2/6) and η , given:
1
1−η

x
y1−η
y1−η 1−η
WTP = (1 − η )[ω (2 / 6)( i − i ) + i )]
1 −η 1 −η 1 −η 

∧
1−η
= [ω (2 / 6)( xi
(5)
1
− yi1−η ) + yi1−η ]1−η
Risk
389.94
219.85
779.01
404.25
606.89
1029.44
212.20
127.93
380.43
160.07
315.78
421.36
Tab.4 WTP t tests
EV
t
P
1
500
4.49
0.00
2
250
2.04
0.04
3
1000
5.03
0.00
4
500
5.18
0.00
5
750
3.93
0.00
6
1250
4.53
0.00
Also, we can find that the willingness to pay
increase with the expected loss. This shows that people’s
worry about environmental risks is positively related to
the expected harm of these risks, which shows a
fundamental rationality in risk perception and decision
making. Correlational analyses show that there is a
significant positive correlation between WTP and EV for
the majority of subjects (71 out of 75).
Gender difference has long been found in
environmental risk perception [25]. This current study also
pays attention to how male and female subjects perceive
environmental risks differently. Tab. 5 shows the
descriptive statistics of male female subjects’ willingness
to pay for the six risk scenarios.
3 Results
3.1 Environmental risk preference
Subjects’ willingness to pay to avoid the six water
pollution risks can directly show their perception of
environmental risks, and manifest their risk preferences.
Also, comparing willingness to pay with the expected
health loss caused by a certain environmental risk, we
can find out people’s risk preference in the context of
environmental risks. When his willingness to pay is
greater than expected value of environmental health loss,
a subject is averse to risk; otherwise, he is risk tolerant.
Tab. 3 presents the mean and standard deviation of
willingness to pay for each risk, where EV is the
expected health loss. It can be found from the above
table that the mean of willingness to pay is smaller than
the expected value of health loss. This implies that
people are generally risk tolerant when it comes to
environmental health risks. Such a risk preference in the
loss domain is in line with the prediction of prospect
theory [24].
500
250
1000
500
750
1250
One-sample t-tests support this finding (see table 4).
(3)
We don’t impose any parameter, which allows us to
estimate subjective probability and utility function,
without adding complexity.
After obtaining willingness to pay, we use
iso-elastic utility function to elicit the value of η ,
Tab.3 Descriptive statistics of WTP
EV
Mean
STDEV
Tab.5 Descriptive statistics of WTPs of male and female
subjects
Male
Female
Risk
Mean
STDEV
Mean
STDEV
1
393.17
204.33
387.53
220.24
2
225.71
127.45
215.48
129.62
3
753.17
353.73
798.24
402.19
4
409.49
170.39
400.36
153.88
5
567.38
315.71
636.30
316.31
6
961.01
454.41
1080.36
392.67
It can be found in the above table that the mean
WTP of male subjects is greater in some risk scenarios,
but less in other scenarios than that of female subjects.
This implies that there is no consistent direction of
gender difference in environmental risk perception.
Further, independent sample t tests show that gender
difference is not significant when it comes to the
willingness to pay (see Tab. 6).
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Tab.6 Independent sample t tests for gender difference
Risk
t
P
1
0.11
0.91
2
0.34
0.73
3
-0.51
0.62
4
0.24
0.81
5
-0.93
0.35
6
-1.22
0.23
3.2 Subjective probability
People perceive environmental risks with subjective
probability rather than objective probability. Existing
studies have shown that subjective and objective
probability can be distinctly different [26-27]. All the
environmental risk scenarios in our study have a
probability combination of (2/6, 4/6). Through nonlinear
least squares we can elicit the value of subjective
probability corresponding to objective probability 2/6.
Tab. 7 presents the descriptive statistics of ω(2/6).
Tab.7 Descriptive statistics of subjective probability
ω(2/6)
Mean
STDEV
Median
Total
Female
Male
0.55
0.54
0.55
0.06
0.06
0.06
0.53
0.52
0.55
The above table shows that the mean value of
subjective probability of 2/6 reaches 0.545. This is much
larger than 2/6. It turns out that people overestimate the
probability of environmental risks. Given the fact that we
show the objective probability of environmental risks,
this implies that people perceive the probability of
environmental risks in a subtle way.
Pair-t test shows that there is no significant
difference between female and male subjects in
subjective probability (t=1.010, p=0.316). It suggests that
there is no gender difference in probability judgment in
environmental risks.
The following table shows the correlation between
subjective probability and willingness to pay for
environmental risks in every risk scenario. It is found
that there is a significant positive correlation between
subjects’ willingness to pay and their judgment of the
subjective probability of the risks. This implies that the
higher the perceived probability, the more willing people
are to take proactive actions.
3.3 Elasticity of marginal utility
Elasticity of marginal utility measures the curvature
of utility function. For environmental risks, it shows how
quickly people get worried as the harm of environmental
risks increases. The larger the value of elasticity of
marginal utility is, the more risk-averse people are. The
exact value of elasticity of marginal utility is important
in both empirical and normative senses.
Following the iso-elastic utility function of formula
(4) and the econometric formula (5), we elicit the value
of elasticity of marginal utility in the domain of
environmental losses. The following table presents the
descriptive statistics of it.
Tab.9 Descriptive statistics of
Mean
STDEV
Total
Female
Male
0.47
0.46
0.47
0.09
0.09
0.08
Median
0.45
0.44
0.46
Tab. 9 shows that the mean value of elasticity of
marginal utility is only 0.468. This is a value much lower
than those used in studies listed in Tab. 1. The highest
observed value of elasticity of marginal utility in the
sample is 0.68, while the lowest value is 0.32. This
shows that elasticity of individual marginal utility only
varies within a small range. The relatively small value of
standard deviation in Tab. 9 shows the low level of
individual difference.
A closer look at the sample shows that there are 12
subjects whose revealed a value elasticity of marginal
utility between 03 and 04. 41 subjects revealed a value
between 0.4 and 0.5. 13 subjects gave a value between
0.5 and 0.6. And only 9 subjects have a value more than
0.6.
Pair-t test shows that gender difference in elasticity
of marginal utility is not significant (t=0.424, p=0.673).
This is consistent with the insignificant gender difference
in willingness to pay and subjective probability.
Correlational analysis shows a significant positive
correlation between subjective probability and elasticity
of marginal utility (γ=0.929, p=0.000). Further, we find
that elasticity of marginal utility is also strongly
correlated with willingness to pay in every
environmental risk (see Tab. 10).
Tab.8 Correlation between WTPs and subjective
probability
Risk
Correlation
P value
coefficient
Risk 1
0.39
0.00
Risk 2
0.48
0.00
Risk 3
0.94
0.00
Risk 4
0.63
0.00
Risk 5
0.49
0.00
Risk 6
0.79
0.00
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Tab.10 Correlation between WTPs and
elasticity of marginal utility
Risk
Correlation
P value
coefficient
Risk 1
0.65
0.00
Risk 2
0.50
0.00
Risk 3
0.81
0.00
Risk 4
0.58
0.00
Risk 5
0.35
0.00
Risk 6
0.80
0.00
4 Conclusions
Elasticity of marginal utility is pivotal parameter in
determining the social discount rate. It is very important
to choose a proper value for it. A big value of elasticity
of marginal utility leads to a high discount rate, which
underweights the welfare of future generations; while a
small value of elasticity of marginal utility brings a low
discount rate, which will limit welfare of the current
generation. Elasticity of marginal utility is both
empirically and theoretically important for our society.
The current study stems from the discussion on the
social cost of climate change. Despite the concentration
on environment, traditional studies have either adopted a
value for elasticity of marginal utility out of normative
consideration, or elicited it from data on consumption.
The difference between environmental issues and
household consumption cast doubt upon these studies.
Also, the risks inherent in environment haven’t attracted
the attention it deserves. This study bridges these two
gaps with a special research design. We situated subjects
in the face of environmental risks. These risks have the
same combination of probability and differ only in loss
dimension. Perceived utility was measured through
willingness to pay elicited with bi-section method and
scaled with iso-elastic utility function.
Analyses show that people are risk tolerant in the
face of environmental risks, as their willingness to pay is
lower than the expected harm of risks. And gender
difference is not significant in environmental risk
perception when measured through willingness to pay.
This is different from the findings of traditional studies.
It can be explained by the fact that our approach is based
upon revealed preference, while traditional studies rely
on stated preference. Also, we find that people noticeably
overestimate the probability of environmental risks. The
mean value of subjective probability reaches 0.545,
although subjects are informed that the objective
probability is 2/6. This shows that people are far from
rational when it comes to the perceived probability of
environmental risks. They form subjective probability
judgment in a complex and subtle manner. Further, we
find a positive relationship between subjective
probability and willingness to pay. Those subjects who
perceive higher subjective probability are more willing to
pay money for avoid environmental risks, i.e. they
perceive
higher
threat/negative
utility
from
environmental risks.
We elicit the value of elasticity of marginal utility
with formula (5). The mean value is only 0.468. This
value is much smaller than those found or used in
traditional studies. And we notice that difference between
male and female subjects in elasticity of marginal utility
are insignificant, which means that males and females
are similarly sensitive to the change in the harm of
environmental risks. Besides, individual difference is
quite small in elasticity of marginal utility as shown by
the small value standard deviation. There is a close
relationship between elasticity of marginal utility and
people’s willingness to pay to avoid environmental risks.
The higher the elasticity of marginal utility, the larger the
willingness to pay is.
Our study shows that people’s elasticity of marginal
utility is much lower than formerly estimated. This value
is elicited through people’s environmental decision
making. Hence, it is more consistent with people’s real
attitudes towards environmental problems. As shown in
Ramsey equation, a lower value of elasticity of marginal
utility will lead to a lower discount rate. Replacing the
value of elasticity of marginal utility in some of the
studies listed in Tab.1 with our newly estimated value
0.468, we can get much lower value of discount rate (see
Tab. 11). It can be found that in Tab. 11 that new values
are much lower than former ones.
of
Tab.11 New discount rates with lower elasticity of marginal
utility
Researcher
Weitzman Stern Nordhaus Garnaut [14]
[6]
[1]
[2]
Former
g
2
2
2
0.1
1
1.3
1.5
2
2
Former
6
1.4
5.5
New
2.94
0.71
2.44
0.05
1 and 2
1.3
1.35 and
2.65
0.66
Out study suggests a lower discount rate in the case
of environmental risks. A lower discount rate means that
we need to give more weight to the welfare of future
generations. This finding is based upon behavioral study,
rather than normative deduction. The value of it lies in its
consistency with individual behaviors. Although many
researchers have emphasized that discount rate is a social
problem, different from individual discount rate, this
view neglects that it is micromotives that underlie
macrobehaviors [28]. Besides, recent psychological
studies have shown that people discount future
environmental welfare at very low rates [17]. In some
studies, many people state that they do not discount at all
[29]
. Our research finding can partly explain these
phenomena.
The current research behaviorally elicited the value
of elasticity of marginal utility with a special experiment.
This research design can be used for future research on
this topic. Future researchers can study the real value of
pure time preference with this it by presenting subjects
intertemporal environmental risks. Then they can obtain
the behavioral discount rate for environmental problems.
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