WPS5421
Policy Research Working Paper 5421
The Value of Statistical Life
A Contingent Investigation in China
Hua Wang
Jie He
The World Bank
Development Research Group
Environment and Energy Team
September 2010
Policy Research Working Paper 5421
Abstract
Economic analyses of development projects and policies The estimated income elasticity of willingness to pay is
often involve assigning an economic value to changes in 0.42. Using data on the incidence of cancer illness and
the risk of loss of human life. A typical term used in the death in the population, these willingness to pay figures
economic analyses is the value of statistical life, which imply that the marginal value of reducing the anticipated
reflects the aggregation of individuals' willingness to pay incidence of cancer mortality by one in the population
for fatal risk reduction and therefore the economic value is 73,000 yuan and an average value of 795,000 yuan,
to society to reduce the statistical incidence of premature which are about six and 60 times average household
death in the population by one. Studies on the value annual income, respectively. The big difference between
of a statistical life have been extensively conducted in the marginal value and the average value of fatal risk
the developed world; however, few such studies can be reduction corresponds to a very low estimated elasticity
found for developing countries. This paper presents a of willingness to pay with respect to fatal risk reduction.
study that estimates individuals' willingness to pay for This finding challenges the validity of previous studies
cancer risk prevention in three provinces of China. The of the value of a statistical life, which are mostly based
results imply that the mean value of willingness to pay on average willingness-to-pay values of mortality risk
for a cancer vaccine that is effective for one year is 759 reduction.
yuan, with a much lower median value of 171 yuan.
This paper--a product of the Environment and Energy Team, Development Research Group--is part of a larger effort in
the department to understand and improve environmental governance in developing countries.. Policy Research Working
Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at hwang1@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
The Value of Statistical Life: A Contingent Investigation in China
Hua Wang and Jie He1
JEL classification:
Key words: Value of Statistical Life (VSL), Contingent Valuation, Willingness to Pay,
MBDC, China
1
The authors are Sr. Economist of the Development Research Group, the World Bank, and Assistant Professor
of Department of Economics, University of Sherbrooke. Corresponding Address: 1818 H Street, N.W.,
Washington, DC 20433, USA. Email: hwang1@worldbank.org. The views expressed in this paper are solely of
the authors and do not necessarily represent those of the World Bank, its Board of Directors, or the countries
they represent.
1. Introduction
Economic analyses of development projects and policies often involve assigning monetary
values to human lives, especially in the areas of public health, occupational safety,
transportation, and environmental protection, where human lives can be significantly affected by
a proposed project or policy change. As resources are finite, trade-offs between other resource
uses and reducing risks to life are inevitable. In order to help make rational choices in these
tradeoffs, a concept of value of a statistical life (VSL), as opposed to a specific person's life, has
been defined and extensively studied2. VSL is an economic value which measures the break-even
point at which society as a whole is willing to pay (WTP) in order to reduce the statistical risk of
death.
Extensive VSL studies have been conducted in the industrialized countries, however, few studies
on VSL can be found in the developing world. Almost all of the previous studies indicate that the
VSL estimation results are sensitive to the sectors studied, the estimation methods employed, the
risk reduction levels as well as the demographic and economic characteristics of the studied
population. It is therefore very important to directly estimate VSL for a country of concern.
A significant number of earlier VSL estimates come from studies that measure compensating
differentials for on-the-job risk exposures in labor markets. Since the 1990s, however, the
contingent valuation (CV) method has been widely used to estimate the value of a statistical life.
An individual's WTP for a specified death risk reduction can be elicited with a plausible CV
scenario and a VSL can be estimated by dividing the WTP by the change in death probability.
The advantage of the CV method over the traditional market approach is that a CV study can be
flexibly designed even when no similar markets exist. This nature of the CV approach is
especially important for the developing country context, because a good competitive market can
hardly be found and data on risk and compensation are rarely available in most of the developing
countries. However, the challenges in using the CV method to estimate VSL are enormous.
Beside the conventional challenges in using CV method: questionnaire design, statistical
analysis, strategic responses and elicitation method choices, etc., a particular challenge comes
from the empirical finding that individuals may have difficulties in understanding a numeric
probability change. Our analyses also show that the VSLs obtained from the previous CV studies
which estimated WTPs for a couple of numeric risk reductions are incompatible with the
theoretically defined marginal WTPs. These findings lead to suspicion of the validity and
reliability of most of the previous CV studies for VSL estimation.
A contingent valuation study of health risk reduction was conducted in three provinces of China
in 2000. A VSL can be calculated based upon the WTP information from that survey and the
cancer morbidity and mortality data. In the CV survey, respondents are not asked to evaluate the
abstract probability reduction as done in conventional risk valuation studies, which is usually a
difficult task for the respondents to complete. Instead, they are asked whether or not they are
willing to buy a cancer vaccine that is effective for one year. This CV scenario is easy to
understand and is similar to a market transaction. WTP functions of risk reduction can be
estimated with data of cancer morbidity and mortality, and a marginal value estimation of risk
2
A comprehensive literature review on VSL studies can be found in Miller (1999), Viscusi and Aldy (2003) and
Australian Safety and Compensation Council (2008).
2
reduction can be produced, which is in sharp contrast to the average value estimation of risk
reduction as done in a conventional contingent valuation study.
This paper is organized as follows. In the next two sections, we briefly present a literature review
on WTP for mortality reduction and VSL estimation. The relationship between WTP for
mortality risk reduction and VSL is developed in Section 4. In section 5, we present our
contingent valuation survey. The econometric methods are illustrated in section 6, and the data
and the estimation results are presented in section 7 and 8. VSL calculation and simulation are
presented in section 9. We conclude the paper in section 10.
2. VSL Estimation Methods
VSL estimation methods can be categorized into two types.3 The first type of methods measures
the loss of direct income. One representative approach is the so-called human-capital method,
which calculates the present value of future income forgone due to a premature death. These
approaches however have two well recognized short-comings. First, they do not take into
consideration the intangible impacts on individual and family well-being such as suffering and
loss of leisure, therefore are often regarded as the lower bound of the social cost. Second, these
approaches only focus on the active population but ignore the value of children and aged people.
The second type of approach measures willingness to pay or accept changes in human mortality
risk. The principle of this type of methods is to use people's preferences as a basis for the
measurement of increase (or reduction) in human well-being related to the reduction (or
increase) of mortality risk (World Bank, 1998). As the "consumer surplus" from living can be
many times higher than human capital, studies using the willingness-to-pay approach generally
give a higher valuation of life than those using direct income losses. Using surveys in Taiwan
and Los Angeles, Alberini and Krupnick (2000) found the WTP estimates gave values 1.61-2.66
times higher than the loss of direct income.
There are two ways of empirically estimating individuals' WTP for mortality risk reduction: the
revealed preference approach, which can use compensating wage or consumer behavior data, and
the stated preference approach, such as the contingent valuation method (Krupnick et al., 2002).
The revealed preference approach often uses differences in wage rate to measure compensations
that people require for differences in risk of dying or falling ill caused by occupational hazards.
Viscusi and Aldy (2003) provide a comprehensive survey of compensating wage studies in the
US and other countries. The recommended VSL figures range from 4 to 9 million dollars for the
US case and 0.8 to 74.1 million dollars for other countries.
Besides the sensitivities of the estimation results to the studied sectors or markets, the VSL
estimation with the revealed preference approach also suffers from some other serious
limitations. First, in the labor market or durable goods consumption markets, inactive population,
especially the elder people, cannot be included. Secondly, workers in the labor market may not
be perfectly aware of the workplace risk. Thirdly, this approach also implicitly assumes that
3
A detailed introduction of the various approaches using the loss of direct income can be found in World Bank
(1998).
3
people have no preference for certain profession choice, which is not true in some of the cases.
Finally, many labor market hedonic studies also suffer from measurement errors. Workers within
an industry or occupation group are typically assigned with the same workplace fatality rates, but
in reality, the fatality rates can be quite different for different people even working in a same
industry.
The contingent valuation (CV) method is a stated preference approach. It uses surveys to ask
individuals to report directly their WTPs for a specified and hypothetical reduction of risk of
premature death. An obvious advantage of the CV method over the hedonic price approach is
that the former has more flexibility in choosing a population and a specific type of risk (Alberini
and Chiabai, 2007). However, a well-behaved CV analysis is more demanding for technical
expertise in questionnaire design, sample choice, treatment of responses, etc. The biggest critic
of this method is that it is hypothetical, which requires a researcher using this method to
undertake additional efforts to remind people of other related factors such as real budget
constraints.
3. VSL Estimation in Developing Countries
Although numerous VSL studies have been conducted in the U.S. and other developed
countries4, there are few studies directly conducted in the developing world. Three types of
efforts have been made in order to obtain a VSL estimate in a developing country: scaling, meta-
analysis and direct estimation (Bowland and Beghin, 2001). The scaling approach adopts
valuation estimates made in developed countries with calibrations based on income differences.
However, the scaling approach is often problematic as per capita income level is not the sole
determinant of VSL, because other factors such as regional economic and demographical
characteristics and cultures can also affect VSL (Mead and Brajer, 2006). Besides, income
elasticity is not constant. Chestnut et al. (1997) and Alberini and Krupnick (2000) indicated that
in most of the cases, the VSL's income elasticity is higher for poorer people than for the richer
one. The survey made by Viscusi and Aldy (2003) of the studies conducted in the developed
countries revealed an income elasticity of 0.5 to 0.6 , while Bowland and Beghin (1998) found
an elasticity of 1.8 for the developing countries studied.
The meta-analysis of VSL uses existing studies conducted in the industrialized countries to
derive a VSL prediction function for developing countries, taking into considerations of
differences in risk, income, human capital levels as well as demographics of a country. For
example, Bowland and Beghin (2001) analyzed over 40 wage-risk studies conducted in the
industrialized countries, and found VSL not only depends on income level but also on other
factors such as average age, education level, coverage degree of social security system, and other
social situation. Based on their estimation models and available data in Santiago, Chile, they
predicted the cost of mortality due to air pollution for this South American city.
However, even the meta-analysis approach is still problematic to developing countries. Some
specific factors in a developing country, such as distorted wages, cross-subsidy of public
services, difficulties in valuing various homemaking services, high unemployment rates, are
obviously contradictory with some implicit assumptions made in the original studies such as the
4
A summary table of the study results is presented in the appendix.
4
existence of a perfectly competitive labor market for a wage-risk hedonic study. In addition,
these studies often have to ignore the potentially important roles played by age and health status
in mortality risk reduction valuation (Krupnick et al. 2002; Arberini et al. 2004 and Hammitt and
Liu, 2005). Given the fact that people living in different countries do not necessarily share the
same demographical structures and health characteristics, the simple scaling principle or the
independent-variable-based scaling principle do not permit us to include the differences existing
in the original mortality risk between the countries. Chestnut et al. (1997), based on two
paralleled CV studies in Bangkok and Los Angeles, revealed that the differences in the average
increase in the incidence rate for certain respiratory diseases with the same percentage increase
of pollution are incomparable between the two cities.
Obviously if it is feasible, it is always preferable to conduct VSL studies directly for a country
itself. A small number of contingent valuation studies have been designed and carried out in
developing countries to estimate VSL. Alberini et al. (1997), Alberini and Krupnick (2000),
Hammit and Graham (1999), Hammit and Liu (2004), and Bhattacharya et al (2007) are a few
examples. Only until very recently a couple of contingent valuation studies have been conducted
in China to estimate VSL. Wang and Mullahy (2006) conducted a CV study in Chongqing to
estimate WTP for reducing the risk of fatality due to air pollution and the value of a Chinese
statistical life. Based on the face-to-face interviews of 550 individuals in 1998 with an open-end
WTP question format backed by a bidding game in case of respondent's hesitation, a probit
estimation and bootstrap process gives an estimate of medial WTP for saving a statistical life to
be 286,000 yuan, or 34,458 US dollars. Hammitt and Zhou (2006) estimated WTP values for
three health endpoints: cold, chronic bronchitis and fatality, based on an in-person interview
conducted in 1999. The survey was carried out in three locations: Beijing, Anqing and the rural
areas near Anqing. WTP was elicited by a double-bounded, dichotomous-choice format. Each
respondent was asked whether she/he would purchase a treatment which provides a stated risk
reduction at a specified price. After the two dichotomous-choice questions, the respondents were
asked to state their maximum WTP for the risk reduction in an open-ended follow-up. Their
estimations gave a sample-average median value of a statistical life ranging between 33080 yuan
to 140590 yuan ($4000 to $17,000). Both studies only concentrate their surveys in a
geographically limited regions, therefore the conclusion cannot be simply extrapolated to other
regions, given the great regional disparities between different provinces. Both surveys related
their mortality reduction WTP questions directly to environmental quality improvements.
Although the studies reminded respondents to only evaluate their mortality risk reduction
contributed by environmental quality improvements, the respondents might not have totally
excluded from their valuation other benefits caused by pollution reduction. The vast differences
in the estimation results call for further investigations.
4. Contingent Valuation of a Statistical Life
The linkage between a WTP for fatal risk reduction and VSL can be constructed from a life-
cycle consumption model with an uncertain lifetime (Yaari, 1965; Sherpard and Zeckhauser,
1982; Cropper and Sussman, 1990). Following Alberini et al. (2004), the life-cycle model can be
summarized below.
5
A person at the beginning of period j (age j) receives expected utility of Vj over the remainder of
his lifetime.
t T
V j q j ,t (1 ) j t u t (C t ) (1)
t j
ut(Ct) is the utility of consumption in each period t that this individual can receive. To get its
present value, we can multiply it with the probability that the individual survives to that period
qj,t and then discount it to the present at the subjective rate of time preference, .5
In the life-cycle consumption model, Vj is maximized subject to initial wealth, Wj, and a budget
constraint that reflects opportunities for borrowing and lending. The two cases usually
considered are the case of actuarially fair annuities and the more realistic situation in which the
individual can borrow and lend at the riskless rate r, but can never be a net borrower.
t
yk Ck
Wt W j k j
0 (2)
k j (1 r )
Where y is income and C is consumption. We can use the life-cycle model to determine the
amount of initial wealth that an individual would give up to reduce Dj, the probability that he dies
during the current period. A reduction in Dj will increase the probability that the person survives
to all future periods since, by definition, qj,t is the product of the probabilities that the individual
does not die in all periods from j to t-1,
qj,t = (1-Dj)(1-Dj+1) . . . . (1-Dt-1). (3)
The rate of substitution between Dj and Wj, which keeps the expected utility Vj to be constant,
corresponds to the value of a statistical life for a person of age j, VSLj,
VSLj = (Vj/Dj)/( Vj/Wj) = dWj/dDj . (4)
dWj represents the amount an individual is willing to pay for the reduction in Dj. VSL is the
marginal value of a risk change, as defined in equation (4).
In contingent valuation studies on VSL, an individual is usually presented with a small risk
reduction (D), and a WTP for this small risk reduction is elicited. Because the proposed risk
reduction is small, the VSLj, as defined in equation (4), can be roughly equal to the average WTP
of the risk reduction (Albrini et al, 2004); i.e.,
VSLj = WTPj/Dj . (5)
5
qj,t shows the mortality rates of the individual in the period from j till T. These mortality rates surely depend on the
health situation of the individual at the beginning of the period j. Therefore, in certain sense, the qj,t should be
personalized by the health status of each individual.
6
However, the contingent valuation estimates of VSL, which are based on equation (5), can have
significant biases from the theoretically correct estimates as defined in equation (4). First, the
proposed risk reduction in a CV study cannot be too small in order to be sensible to the
respondents. Therefore the approximation of equation (5) to equation (4) can be a question in
reality. Secondly, it can be a difficult task for a respondent to calculate his/her WTP for a small
risk reduction. A systematic error may exist in a WTP calculation with an individual.
Previous empirical studies find that the VSL estimates as defined in equation (5) are sensitive to
the scales of the risk reduction proposed in CV studies. WTP estimates are found not
proportional to the level of risk reduction. Krupnick et al. (2002), Alberini et al. (2004) and
Alberini and Chiabai (2006) studied the VSLs for USA, Canada and Italy with the CV approach
for two different levels of mortality risk reduction, with one to be 5 times the other, but found
that the WTP is not 5 times high, and therefore different VSL estimates can be produced for a
same sample of population.6 Similar findings are also reported in Muller and Reutzel (1984),
Vassanadumrongdee and Matsuoka (2005), Hultkrantz et al (2006), and Corso et al. (2001),
Andersson and Svensson (2008), Bhattacharya et al. (2007), where WTP increases less than
proportionally with the size of risk reduction. Hammit and Graham (1999) provided a synthetic
analysis for the 19 CV studies published before 1995 that have employed more than one level of
risk reduction in the surveys, and found that, although many studies did find an increasing trend
of WTP with risk reduction, none of the 19 studies shown the proportionality between WTP and
the proposed risk reduction. Persson et al. (2001) elicited WTP information for risk reductions of
10, 30, 50 or 99 percent of mortality risk for one year and provided a graphical relationship
between WTP and absolute mortality risk reduction. They find that WTP is increasing with the
level of risk reduction but the increasing rate is decreasing.
No theoretical studies have been found on the relationship of WTP with risk reduction. While a
theoretically-correct functional form of WTP with respect to risk reduction is believed to be
dependent on the utility function and the wealth function as presented in equations (1) and (2)
above, one can project that it is an increasing function and to be concave when the risk reduction
level is high enough due to the budget constraint.
To overcome the shortcomings of contingent valuation studies in estimating VSL as discussed
above, it is logical to require researchers to estimate functional forms of WTP with respect to
risk reduction and to derive a marginal WTP estimate of risk reduction. This study represents
such an effort, where marginal WTPs are estimated and simulated with different WTP functional
forms, and the results are compared with the average WTPs of risk reduction.
5. The Health Survey
In 2000, we conducted a household survey on public health and environment in three rural areas
in China: Danyang (Jiangsu Province), Liupanshui (Guizhou Province) and Tianjin suburban. In-
person surveys, where respondents complete the questionnaires with close guidance from
enumerators7, are conducted. About a half of the sample is workers who were working in local
6
In Alberini et al. (2004), the mean WTPs for 1/10000 and 5/10000 risk reductions are $370 and $466 in Canada,
and $487 and $ 770 in the United States.
7
The major intention is to minimize the potential interviewer bias. The interviewers read another copy of identical
questionnaire to the respondents, but can not directly work on the questionnaire, and the respondents do not need to
7
township-village enterprises. One to three workers were randomly selected from each factory
based on the worker name list and were invited for personal interviews. Another half of the
sample is rural household heads, or farmers, who were interviewed in or around their houses. A
list of communities was first randomly selected in the three municipalities, and a certain number
of household interviews were assigned to each selected community. Teams of enumerators were
sent to the communities, and the enumerators knocked the doors of the households selected and
invited the heads of the households to participate in the interviews. If the heads of the households
were not at home or refused to be interviewed, the neighbor households were then selected, until
the total number of interviews in this community reached the target number.
The questionnaire was developed from a similar questionnaire previously employed in China,
and was pre-tested in each of the municipalities. Special cares were paid to the WTP section of
the questionnaire. Several group discussions and two pre-tests were conducted at each of the
three study areas, focusing on the wording of the WTP questions as well as the price range. The
survey was conducted by teams of researchers, professors and graduate students, and the survey
teams were first trained by one of the authors of this paper, and then participated in the group
discussions and the pre-tests of the questionnaire in order for them to fully understand the issue
and to get familiar with the task before the formal surveys started. The final version of the
questionnaire includes seven parts: personal characteristics, environmental perceptions and
attitudes, local pollution control issues, pollution impacts on respondents and their families,
household situation, health status, and finally the contingent valuation questions about cancer
prevention.
The willingness-to-pay question on health risk reduction is posed in the form of cancer risk
prevention. Aiming to obtain detailed information about the attitudes of each respondent toward
the proposed cancer vaccine, we use a Multiple Bounded Discrete Choice (MBDC) format to
check about respondent's WTP. This format combines two aspects of development from the
traditional dichotomous choice (DC) WTP question. On one hand, it allows respondents to vote
on a wide range of referendum thresholds, and on the other hand, a scale of "polychotomous
choice" response options from "Definitely No" to "Definitely Yes" is also provided to allow
respondents expressing their levels of voting certainty for the referendum at each price level. In
this way, MBDC survey technique actually reinforces both quantity and quality of CV data8.
The WTP question in our questionnaire is as follows:
"Suppose there is a medicine that can prevent you from getting cancer for one year with one
dose. There would be no side effects. But after one year, the medicine will fully stop functioning. With
given quality and impact, the price of the medicine could be different. We would like to know the
possibility for you to buy such a vaccine, with different prices, to make sure you would not fall ill of
cancer for one year.
speak out their answers to the interviewers. But just like with a mail survey, the final quality of the questionnaire
completion can not be controlled by the enumerators.
8
For more discussions, see Wang and He (forthcoming).
8
Please note that, 1) different people have different probabilities to fall ill of cancer. Therefore, the
likelihood that different people truly need the medicine is different. If a person will surely not get
cancer in the next year, he may not need this preventive measure; and 2) with a given income, a person
also needs to buy other goods and services such as food and clothes, and may spend money to prevent
from other diseases.
We only want to know the likelihood that you would buy such a medicine, given the following list of
prices, to make sure you would not fall ill of cancer in the next year. There is no right or wrong
answers; we only want to know how you would react to the different prices. Please select one
possibility under each price given below."
Price Definitely not Probably not Not sure Probably yes Definitely yes
Free(0 yuan)
)
10 yuan
20 yuan
40 yuan
60 yuan
90 yuan
150 yuan
200 yuan
300 yuan
500 yuan
1000 yuan
2000 yuan
5000 yuan
8000 yuan
10000 yuan
15000 yuan
6. WTP Estimation with MBDC Data
MBDC format WTP data, offering rich information with extended bid price choices and multiple
options of certainty levels, have been used in the past in a number of contingent valuation
studies. Several of the studies employing the MBDC data, such as Alberini et al. (2003),
implement an extension of the Random Valuation Model proposed by Wang (1997), which
views the value that an individual attaches to any amenity (including market traded goods) as a
random variable with an unspecified probability distribution (Shaikh et al. 2007). Following this
logic, the data obtained from the MBDC format are several observations of an individual WTP
distribution that is attached to the amenity in question. Wang and Whittington (2005) and Wang
et al. (2004a) further proposed a CV approach called Stochastic Payment Card (SPC). This
approach extends the MBDC format WTP question and directly elicits the numerical likelihood
information of the respondents beside the verbal likelihood information. With this arrangement,
we are able to directly estimate individual valuation distributions from the SPC data provided by
the MBDC format questionnaire.
9
In this paper, we will use an alternative analytical strategy initially proposed in Wang and He
(forthcoming) to estimate individual valuation distributions for cancer risk reduction. This new
approach is based on the random valuation theory as described in Wang (1997) and Wang and
Whittington (2005) and uses a similar data encoding strategy as used by Evans et al (2003).
Subjective verbal likelihood responses given by MBDC respondents are first encoded into
numerical likelihood data, or SPC data. Then the SPC data are analyzed to estimate individual
valuation distributions, as did in Wang and Whittington (2005).
This new WTP estimation strategy suggests that an individual i may not know the exact value of
his WTP for risk reduction but he does have some idea about the range of values in which it lies.
When the proposed bid price comes out to be sufficiently lower (higher) than the value range, he
will be relatively more sure about his positive (negative) answer, but when the bid price is
located close or in the value range, he will be more unsure about his choice. So we can express
an individual i's WTP for risk reduction, represented by Vi, as a random variable with a
cumulative distribution function F(t). The mean value of Vi is i, which represents the mean
WTP of the individual i for the cancer preventive medicine, and the standard variance is i . So
we can write the WTP model as,
Vi=µi+i (6)
where i is a random term with a mean of zero. When given a price tij for the cancer vaccine, the
probability for the person to say "yes" will be,
Pij = Prob(Vi>tij)
=1-F(tij) (7)
Once Pij, the probabilities for individual i to agree on the price tij, is known to a researcher, either
by assigning numerical values to the verbal MBDC data or by directly asking individuals of their
numerical likelihood information as did with the SPC approach, equation (7) can be estimated
for each individual. The estimation model can be constructed as follows:
Pij = 1-F(tij) + i (8)
where the error term i has a mean of 0 and a standard variance of 2. can be constant for a
respondent i, but its value will be different for different respondents. Pij is a dependent variable,
which is the certainty answer chosen from "definitely yes" to "definitely no" by a respondent i at
price j. Pij will take values between 0 and 1, with the value approach to 1 meaning a higher
certainty of accepting and the value approach to 0 meaning a lower certainty. These values can
be viewed as a continuous variable. tij is an independent variable, which is the bid price proposed
in the questionnaire. We can also consider tij as a continuous variable.
Assume a specific functional form for Fi(·), such as of a normal distribution, with a mean i and
tij i
a standard variance i , i.e., F (tij )
, then model (8) can be written as,
i
tij i
Pij 1 i
(9)
i
Assume i also has a normal distribution. Then,
10
tij i
Pij 1
i
N(0, 1).
and the log likelihood function is:
t i
P 1 ij
J ij
i
log
Log Li = j 1
(10)
This is equivalent to a least square nonlinear estimation; has no influence on the estimation, as
long as it's a normal distribution. With the log likelihood function (10), i and i can be directly
estimated for each individual i with the MBDC data.
Once i is estimated for each individual, models can be constructed and estimated to analyze its
determinants. One simple example is to have the following linear functional form:
i= 0 + xi' + e1 (11)
where x are personal specific characteristics. s are coefficients to be estimated; e1 is a random
errors.
7. Survey Data Analyses
7.1 WTP Responses
1,933 respondents accepted to be interviewed. 594 respondents did not give positive answers
(i.e., a "not sure", "probably not" or "definitely not" answer was selected) at the price of zero,
which may reflect that the respondents do not think they would need this preventive medicine. At
the other end, 205 persons did not give negative answers (i.e., definitely yes, probably yes or not
sure was selected) even at the highest bid price, 15,000 Yuan, which means that the price range
did not cover the whole WTP range if people answered the questions honestly. 9 838 respondents
have their WTP located in the price range. Two respondents have cancer so the preventive
medicine is not meaningful to them. 135 respondents did not fully complete the questionnaires,
and 146 respondents gave some unreasonable answers to the likelihood questions, such as giving
a higher acceptance probability for a higher bid price10. Those responses would have been
corrected by the enumerators if it is a traditional in-person interview. Table 1 summarizes the
statistics of the responses.
7.2 Characteristics of the Respondents
9
Almost all members in the focus group and pre-tests believed 15,000 Yuan to be more than the highest possible
WTP for a medicine preventing cancer for one year. But apparently, some people may have very high WTP for such
a medicine if they give honest answers.
10
This may make sense in reality if people believe that a higher price means a higher quality.
11
Table 2 reports the descriptive statistics of the respondents in three categories: 1) 594
respondents who give negative answers at the zero bid (no demand); 2) 205 respondents who are
positive even at the highest bid (extremely high demand), and 3) 838 persons whose WTPs are
covered by the bid range (normal demand). The sample statistics are given in the third column.
The stars marked in the first three columns indicate the significant difference of the variable
from the category 3, which will be used in the following econometric analysis.
In Table 2 we can see that the observations in category 3 with normal demand share very similar
statistical characteristics with the whole sample. The only variable that seems to have a
significant difference is the income uncertainty in future 5 years. When there are statistical
differences between the subsamples, we generally believe these differences are logical: people
who have answered negatively at the zero bid generally have lower income level, fewer cases of
cancers observed in their families and relatives, lower degree of trust or need for such a
medicine. People reporting positive answers at the highest bid, on contrary, have much higher
income level, more frequent cases of cancers observed in their families and relatives, high degree
of trust or need of such a medicine. These findings are further supported by the Probit analyses
reported in Table 3, where the probability for a respondent to report a negative answer at zero bid
and the probability for a respondent to report a positive answer even at the highest bid are
modeled, with respect to the respondents in category 3 whose WTP is covered by the payment
range. The statistically significant independent variables are family income (and the future
income uncertainty for the case of negative answer at the zero bid), relatives diagnosed with
cancer, and the two dimensions of perception measurements of people on the preventive
medicine: trust and need. However, other socio-demographical variables, such as age, sex,
profession, health habits and religion, etc., do not show significant differences. This implies that
the survey respondents do base their WTP answers on their payment capacities, their real needs
and trust in the medicine.
7.3 WTP Response Statistics
The frequencies and the percentages of WTP responses of the whole sample (including all of the
three categories) are presented in Tables 4-1 and 4-2. Based on Table 4-2, inverted stochastic
demand curves for the whole sample can be drawn. Tables 5-1 and 5-2 show the frequency
distribution and the percentage distribution of responses of respondents with normal demands.
As shown in Table 5-1, the percentage of "definitely yes" answer is decreasing fast from 70.29%
at the price of zero to less than 0.2% at the price of 8000 yuan. While the percentage of
"definitely no" answers increases steadily with the price offered, from 0% at price of zero to
about 87.7% when the price increases to 15000 yuan. In total, over 37% of the responses are
uncertainty responses (probably yes, not sure, probably not) which happen between the prices of
90 and 1000 yuan. This indicates that the respondents have relatively important uncertainty in
their WTPs. This, to certain degree, justifies the use of MBDC format and reveals the existence
of individual WTP distribution.
8. WTP Estimation Results
12
8.1. Individual WTP
To estimate the mean WTP, i, for each of the 838 respondents whose WTP distribution is
covered by the MBDC price range, we conduct maximum likelihood estimations with normal
distribution functions as shown in equation (4). All redundant answers at the two ends of the
payment card, i.e. those "definitely yes" answers at the prices below the highest price where a
"definitely yes" answer is given and those "definitely no" answers at the prices above the lowest
price where a "definitely no" answer is given, are deleted. After doing so, each respondent has 2
to 11 answers getting into the maximum likelihood estimation.
The benchmark encoding strategy for the verbal likelihood data is to use 0.999 for "definitely
yes," 0.75 for "probably yes," 0.50 for "not sure," 0.25 for "probably no," and 0.001 for
"definitely no".11 Wang and He (forthcoming) tried other encoding strategies and found the
estimation results were relatively stable if a symmetrical encoding strategy was used. The same
conclusion is drawn in Evans et al (2004). In the following discussions only the results based on
the benchmark encoding strategy will be presented.
The distributions of the estimated mean value of individual WTP (i) are given in Table 6-1. The
mean WTPs vary from 0.27 to 11,872.18 Yuan, with a sample mean of 759 yuan (or, 5.6% of
sample average household annual income) and a medium value of 172 yuan.
8.2. Average WTP for Risk Reduction
With the estimated individual WTPs and the expected cancer risk reduction for each individual,
an average value of cancer risk reduction can be calculated for each individual, and a sample
mean value can be obtained. This sample mean value corresponds to the VSL estimate in a
conventional contingent valuation study for mortality risk reduction. The morbidity-based
average value of risk reduction is corresponding to a lower bound of VSL and the mortality-
based value corresponding to an upper bound. The reason is that the cancer morbidity risk is
always higher than the cancer mortality rate: falling ill of cancer does not necessarily mean
dying, but not falling ill of cancer means that the individual will not die of cancer. The
morbidity-based average value is in fact the value of cancer, which should be lower than the
value of life. The WTP divided by individual's expected value of cancer mortality corresponds to
an upper bound of VSL, as the WTP obtained in our survey does not only include the WTP for
avoiding death caused by cancer but also include WTP for avoiding suffering and medical
expenditures that may be caused by a cancer.
The mean value of the morbidity-based average value of cancer risk reduction is estimated to be
0.89 million yuan, while the median is 0.18 million yuan, for the group of respondents with a
normal demand of cancer vaccine. The mean value of the mortality-based average value of
cancer risk reduction is 1.97 million yuan and the median value is 0.39 million yuan12. The
11
The values of 1 and 0 cannot be used for the answers of "definitively yes" and "definitely no" because a normal
distribution function is assumed.
12
The results here are only for those respondents with a normal demand of cancer vaccine whose WTP is covered
by the payment card. Those who do not need a vaccine as described in the survey cannot be included in the analyses.
This is a shortcoming of such a study, which is similar to the hedonic wage studies that cannot include those people
13
distributions of the average value of risk reduction by age and sex are presented in Tables 6-2
and 6-3. In general, a female values more than a male. A younger person values more than an
older person.
8.3. WTP Determinants
The estimated WTP means, i, can be further analyzed with a simple robust OLS regression on
log WTP, as shown in equation (11), in order to see how the demographical, economical, social
and health characteristics of a person can affect his/her WTP. The estimation results are reported
in Table 7. The regression gives consistent results for almost all of the variables. People having
higher family income, with better education, having relatives diagnosed with cancer, having less
future income uncertainty, having regular health check-ups, have relatively higher WTPs. The
WTP is also positively associated with the degree of trust and subjective judgment on the need of
the medicine. The income elasticity of WTP is found to be around 0.42, which is slightly lower
than the estimate provided by Viscusi and Aldy (2003) which is about 0.5 and 0.6 for U.S.
studies. Table 7 also gives the detailed coefficients and their significances for the age-, sex- and
region-related variables. We do not find significant coefficients for the continuous age variable,
which may be due to the fact that the correlation between age and WTP is not a simple linear
one. But we do observe dummies of some age-ranges having interesting, significant coefficients.
In Jiangsu, younger people are willing to pay more, and males are willing to pay more than
females. The opposite is found in Tianjin and Guizhou, where old females are willing to pay
more than old males and younger people. In general, males in Jiangsu are willing to pay more;
old males in Jiangsu and old females in Tianjin and Guizhou are willing to pay the most, and old
males in Tianjin and old females in Jiangsu are willing to pay the least.
8.4. Sample Selection
The empirical results of the WTP model presented in Table 7 can be used to project an average
WTP of the whole sample by substituting the values of the independent variables of all
respondents into the model. The average WTP is estimated to be 439 yuan with a standard
deviation of 546 yuan. The average risk of cancer is 15.5/10000, and the morbidity-based
average value of cancer risk reduction is about 283,000 Yuan. The average cancer mortality rate
is 9.32/10000, and the mortality-based average cancer risk reduction is about 471,000 yuan.
These estimates are lower than the estimates presented in section 8.1. One reason is that the WTP
model used is in log term and therefore the average WTP projected by the model is compatible
with the geometrical mean, rather than the algebra mean. When the WTP is in log terms, those
large values in WTP play less influence in the mean estimation. When a linear WTP model is
used, the estimates are compatible with the results for an average person presented in last
section. This indicates again that the final outcomes are very sensitive to the choices of models if
WTP models are used to project the final estimates.
who are not involved in the labor market studied. Those respondents with extremely high demands of the vaccine,
whose WTP values should be higher than 15,000 yuan, are not included in the estimation either. So the estimates
obtained here are conservative ones.
14
While the log WTP models can significantly under estimate the final values, they can be
employed to assess the potential biases that may be caused by excluding those outliers in our
sample. The average WTPs can be projected for the groups of people with no demand as well as
extremely high demand by the empirical WTP model. The results are summarized in Table 8.
Higher VSL estimates are obtained when those people with extremely high demands are
included, just as expected. When the empirical WTP model, which is estimated with the sample
with a normal demand, is applied to the whole sample, the VSL estimates are slightly lower than
but very close to the ones obtained with the normal sample.
9. Marginal Value of Risk Reduction
In our study, WTP functions of risk reduction can be constructed and estimated, because the
level of risk reduction for each respondent is different. As discussed before, the risk reduction in
our study is the cancer morbidity and mortality rate that each individual is facing. The estimated
WTP function of risk reduction can be used to simulate the marginal value of risk reduction, as
shown in equation (4), which is a theoretically correct valuation. The estimated WTP function of
risk reduction can also be used to simulate the average value of risk reduction, as defined in
equation (5), which is an approximate value given by a conventional contingent valuation study.
The results can be compared.
The estimated relationships between WTP and risk reduction are presented in Table 9-1 for
cancer morbidity rate and in Table 9-2 for cancel mortality rate. The cancer morbidity data are
region-, sex- and age- specific, but the cancer mortality data are available only at the national
level13. The individual cancer morbidity rate and mortality rate are found to be significant
determinants of their WTP for the risk prevention. This implies that our respondents do have a
reasonable judgment of relative cancer risk and do base their WTP answers on the risk judgment.
The results of six modeling strategies are presented in Tables 9-1 and 9-2. In model 1, the WTP
is forced to be proportional to the risk reduction; i.e., WTP=a*RR, where RR is risk reduction
and a is the coefficient which is individual specific. In theory, when risk reduction is very small,
this should be the case. The marginal value and the average value of risk reduction with model 1
are the same, and the estimation result are 226,700 yuan for morbidity risk and 282,843 yuan for
mortality risk for an average person, who takes the sample average values for all related
variables in the model except WTP and RR.
In model 2, the WTP model is specified as WTP = a*RR + b*RR^2. The log likelihood test
shows that model 2 is a significant improvement over model 1. Income turns out to be a
significant variable. For an average person, the marginal value of cancer is 353,138 yuan and the
average value of cancer is 433,119 yuan. For mortality risk reduction, the marginal value is
810,879 yuan and the average value is 572,023 yuan.
In model 3, it is assumed that individuals may have errors in judging their WTPs, and this error
is determined by individual characteristics. The model is specified as WTP = a*RR + c.
13
The national-level cancer morbidity data are used for the respondents in Guizhou as the data for Guizhou are not
available.
15
According to the log likelihood values, model 3 is a significant improvement over model 1,
however, the marginal value estimate is much lower with model 3 and even negative for
mortality risk.
In model 4, individual errors in both risk reduction judgment and WTP calculation are
considered. The model is specified as WTP= a*RR + b*RR^2 + c. The results are much better
according to the log likelihood values. The significant variables include the risk reduction, the
square of the risk reduction and the personal characteristics. For an average person, the marginal
value of cancer is estimated to be 68,410 yuan and the average value of cancer is estimated to be
514,386 yuan. For mortality risk reduction, the marginal value is 72,616 yuan and the average
value is 794,692 yuan.
Model 5 tests the overall significance of including the interactions of risk reduction with personal
characteristics, and it is found that the interaction is not significant.
Model 6 gives another version of model 5, but the dependent variable in model 6 is log WTP;
i.e., log(WTP) =a*RR + b*RR^2 + c. The interactions of risk level with personal characteristics
are also tested, which did not show a significant improvement. The marginal value and the
average value of cancer are estimated to be 29,208 yuan and 110,801 yuan for an average person
respectively. The marginal value and average value of mortality risk reduction are 25,787 yuan
and 183,385 yuan respectively. Because the dependent variable is in log term, the values
estimated are corresponding to the medial value of the WTP in the sample.
In general, the results presented in Tables 9-1 and 9-2 are consistent, but the model performance
presented in Table 9-2 is lower than that presented in Table 9-1. It is understandable because the
results presented in Table 9-2 are for mortality risk reduction which is only based on a national-
level dataset that has no variation between regions.
Model 4 and 6 are the best among the alternative models. Model 4 in Table 9-1 gives a value of
cancer of 68,410 yuan with the marginal value approach and 514,386 yuan with the average
value approach. Model 4 in Table 9-2 gives a VSL of 72,616 yuan with the marginal value
approach and 794,692 yuan with the average value approach. One can see a tremendous
difference between the results obtained from the marginal value approach and the average value
approach.
Our results are in contrast to those results previously obtained in China. Wang and Mullahy
(2006) provided an estimate of medial WTP for saving a statistical life to be 286,000 yuan in
1998, and Hammitt and Zhou (2006) provided a sample-average medial value of a statistical life
ranging between 33,080 yuan to 140,590 yuan in 1999. Our results are for the year of 2000. The
medial value of statistical life is estimated to be 395,694 yuan with the simple average approach
and 183,385 yuan with the log WTP model. With the marginal value approach, the VSL is
estimated to be 72,616 yuan for an average person. With the average value approach, the VSL is
estimated to be 794,692 yuan for an average person based on the WTP modeling result and1.97
million yuan based on a simple sample average.
16
In order to see how the estimation result changes with the level of risk reduction, we conduct
simulations based on the modeling results of models 4 and 6. Presented in Table 10 are the
simulation results of cancer morbidity risk reduction14. Individual characteristics are fixed at
their sample average values. The simulations show that the average values of risk reduction are
always higher than the marginal values. At the risk reduction level of 1/1000, the WTP model
gives an average value of 11.4 times the marginal value, and the log WTP model gives an
average value of 5.3 times the marginal value. The marginal values do not change much when
the risk reduction is small. However, the average value is decreasing dramatically along with the
increase in risk reduction. This is consistent with the empirical findings that higher VSL
estimates are found when lower risk reduction levels are proposed in contingent valuation
studies.
10. Discussion and Conclusion
In this paper, we present a study on the value of statistical life (VSL) in China which uses data
on cancer morbidity and mortality observed in China and information on willingness-to-pay
(WTP) for cancer risk prevention that was collected in a contingent valuation study conducted in
three areas of China in 2000. The cancer risk information is age, sex and region specific, which
can be mapped with the respondents' characteristics to produce an estimate of cancer risk for
each of the respondents. WTP for cancer risk reduction is elicited with a hypothetical cancer
vaccine that can prevent a person from getting cancer for one year.
With the conventional CV approach, the mean value of individual VSLs based on the cancer
mortality data is estimated to be 1.97 million yuan, or 150 times of average household annual
income, which is 13230 yuan for our sample. Because the WTP in the study is more than for
avoiding death, the value can overestimate the VSL. This estimation can also be significantly
affected by a small group of individuals who value lives extremely high. This mean value is
reduced to about 800,000 yuan, or 60 times of the average household annual income, when it is
calculated by the sample mean WTP divided by the sample mean cancer mortality reduction
(759*10000/9.5). This is equivalent to the total WTP divided by the total lives saved, which is
more relevant to policy analyses. However, the former approach is more compatible with the
VSL definition, which is based on an individual's WTP for risk reduction.
VSL can also be projected with the empirically estimated WTP models by substituting the mean
values of the characteristic variables into the models. The average value approach gives a VSL
estimate of 795,000 yuan, or 60 times of the average household annual income15. The marginal
value approach gives a VSL of 73,000 yuan, which is about 10 times lower than the estimate
obtained with the average value approach. As the marginal value approach is a theoretically
correct approach, this sharp difference provides a strong challenge to the validity of the average
value approach, which has been used widely in previous contingent valuation studies of VSL.
Also note that the WTP function of risk reduction in this study is estimated with cross-individual
data which is based on the variations in WTP and level of risk reduction between individuals. It
14
As discussed before, the modeling results with cancer mortality are poorer than those with cancer mortality. But
the simulation conclusion is the same for both the mortality model and the morbidity model.
15
See table 9-2, model 4.
17
is not clear how the function will change if variations in WTP and risk reduction level for a same
individual are also included in the empirical estimation.
While the projected mean WTP should not be statistically significantly different from the sample
mean value if WTP is used as dependent variable, other types of models may produce
significantly different results. In this study, a log WTP model is estimated and used to project the
individual WTP values, and the projected mean WTP as well as the projected VSL are
significantly lower than the values directly estimated from the sample. With a log WTP model, a
VSL of 26,000 yuan is obtained with the marginal value approach and a VSL of 183,000 yuan is
obtained with the average value approach16. These results challenge the validity of the benefit
transfer approach which intends to transfer the (modeling) results of a study site to a policy site,
because the choice of models can significantly affect the final estimations.
The estimates provided above are only from the part of sample where people have a normal
demand of cancer vaccine. The WTP responses collected with the Multiple-Bounded
Dichotomous Choice (MBDC) format do offer a significant amount of outliers which cannot be
reasonably modeled. Those people with extremely high demands and those people with no
demand of the vaccine are excluded in the final estimates. However, further analyses show that
those outliers are reasonable responses. Those outliers can significantly affect the final
estimation results, and may not be able to avoid in a future study of such type, especially for
those people with no demand in cancer vaccine. This shortcoming is similar to the hedonic wage
approach, which does not work for those who does not present in the studied labor market.
However, the potential biases caused by excluding the two types of people from the final
estimation may not be that serious in this particular study, as the WTP projection with the whole
sample does not give a sensible difference from the part of sample with normal demands of the
proposed cancer vaccine.
The survey was conducted in the year of 2000, and the VSL should have changed significantly as
the income of Chinese families has significantly changed. The WTP models estimated in this
study can be used to adjust the estimates. The survey was conducted in three areas of China
which have a wide range of economic and geographical coverage. However, the sample area
only covers rural areas and small towns; big cities are not included. If one believes that people in
the urban areas of China value reducing risks to human lives higher, the estimates presented
above would be biased downward. Therefore, the estimates presented in this paper may be
conservative.
One unique design feature of this risk valuation study is that people are asked to value a cancer
vaccine, rather than to value a specific number of risk change, which is found to be difficult to
understand by the respondents, as used in a conventional risk valuation study. Our approach,
while being more realistic and plausible to the respondents as it offers a reasonable market
choice, runs risk that the respondents might not know what the cancer risk reductions are and
therefore their WTP might not be sensitive to the cancer risk reduction they are facing. However,
the modeling results on WTP and the estimated cancer risk show that this has not been a problem
in this study; people's WTP are significantly correlated with their expected cancer risk reduction.
16
See table 9-2, model 6.
18
The results of this study reveal that a person who is richer, better educated, doing regular health
checks, facing lower future income uncertainty, having relatives diagnosed with cancer, having a
higher degree of trust in medicine, or feeling a higher degree of need for the medicine, has a
higher WTP in general. VSL estimates are higher for women than men and are higher for
younger people. They are also different for different regions in China.
Even though this study can help to provide a better understanding of WTP for risk reduction and
VSL, as one can see from the analyses above, this study cannot give a conclusive result for VSL
that can be used for policy analyses in China. This study also challenged the validity of some of
the previous CV studies on VSL, such as Wang and Mullahy (2006) and Hammitt and Zhou
(2006). A more systematic research on VSL is warranted.
19
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Zhou, Y. R. (1997). Association between air pollution and hospital admissions in Chongqing. Journal of Mod. Prev.
Med, 24(1): 43-45.
22
Table 1. Statistics of Survey Responses
Category Definition Number of respondents
1 Normal Demand: WTP value covered by 838
the bid price range from 0 to 15000
Yuan
2 No Demand - don't need the medicine 594
even at price of zero
3 Extremely High Demand - need the 205
medicine even at the highest price of
15000 Yuan
4 With missing values or disordered 281
answers
5 Age<16 2
6 Cancer patients 13
7 Total number of respondents 1933
23
Table 2. Descriptive statistics of major variables
Whole No Demand Extreme Normal Demand
Sample (mean High
Variable (mean value) Demand Mean Obs Std. Min Max
value) (mean Dev.
value)
Social and demographical
characteristics
Worker (1=worker;
0.499* 0.463*** 0.607* 0.533 838 0.499 0 1
0=otherwise)
Male (1=male;
0.706 0.746** 0.7679* 0.699 838 0.459 0 1
0=otherwise)
Age (years) 36.820 38.695*** 35.000* 36.323 838 10.746 16 77
Education (1=Secondary
school or higher; 0.938 0.912* 0.976* 0.931 838 0.254 0 1
0=otherwise)
Married
0.840 0.887*** 0.762* 0.827 838 0.379 0 1
(1=married;0=otherwise)
Religion (1=yes; 0=no) 0.091 0.101* 0.095 0.080 838 0.271 0 1
Economic characteristics
Income (household
13230 12614** 24411** 13397 838 8495 600 70000
income last year, yuan)
Yuncertain (1=not sure
about future income; 0.160** 0.195*** 0.071* 0.134 838 0.340 0 1
0=otherwise)
Physical and health
characteristics
Rcancer (1=relative
diagnosed with cancer; 0.095 0.071 0.202*** 0.088 838 0.284 0 1
0=otherwise)
Smoking
0.421 0.465* 0.405 0.421 838 0.494 0 1
(1=yes;0=otherwise)
Healthcheck (1=Regular
0.382 0.359 0.417 0.374 838 0.484 0 1
check-up; 0=otherwise)
Perceptions about the
preventive medicine
Need (1=do not need the
medicine at all, 1.814 1.606*** 1.952* 1.856 829 0.766 1 3
2=somewhat, 3=need)
Length (1=expected
length of the preventive
effect 1=less than 1 1.574 1.594* 1.829*** 1.539 831 0.652 1 3
year; 2=1year; 3=longer
than 1 year)
Trust (1=not at all trust
in the medicine;
2.067* 1.922*** 2.250*** 2.104 836 0.527 1 3
2=somewhat. 3= totally
trust)
Regional dummies
Guizhou 0.310** 0.290*** 0.254*** 0.353 838 0.478 0 1
Tianjin 0.352** 0.273** 0.327 0.309 838 0.462 0 1
Note: The stars are to indicate the statistical significance of the differences from respondents in
category 7, based on the student T test.. *** represents a significance for 1%; ** for 5%; * for 10%.
24
Table 3. Determinants of Extreme Demands for the Medicine
Equation for No Demand Equation for Extremely High
(Probit: 1=no demand even at Demand
price of zero; 0= normal (Probit Model: 1=yes at the
demand) highest price; 0=normal demand)
-0.000 -0.023
Age (0.03) (1.59)
0.220 0.068
Male (1.32) (0.21)
-0.198 0.285
Worker (1.47) (1.08)
0.367 -0.149
Married (1.79)* (0.40)
0.075 -0.275
Smoking (0.49) (0.91)
-0.171 1.898
Income (1.67)* (6.70)***
0.066 0.207
Education (0.23) (0.27)
-0.413 0.521
Rcancer (1.50) (1.57)
0.485 -0.173
Yuncertain (2.93)*** (0.37)
0.058 -0.068
Healthcheck (0.41) (0.26)
0.278 0.208
Religion (1.24) (0.48)
-0.386 0.613
Trust (3.41)*** (2.47)**
-0.423 0.082
Need (4.55)*** (0.51)
Tianjin 1.353 -0.714
(6.54)*** (2.43)**
Guizhou 1.370 -1.713
(6.50)*** (3.79)***
Constant 0.394 -20.948
(0.37) (7.01)***
Observations 1380 913
Absolute value of z statistics in parentheses.* significant at 10%, ** significant at 5%; *** significant at 1%
25
Table 4-1. Statistics of WTP Responses: Frequencies of the Whole Sample
Definitely Probably Probably Definitely
Price Not sure Total
not not yes yes
0 427 78 89 303 740 1,637
10 480 91 94 379 593 1,637
20 518 93 105 357 564 1,637
40 545 100 133 353 506 1,637
60 582 118 149 347 441 1,637
90 618 140 162 329 388 1,637
150 682 169 196 275 315 1,637
200 732 188 203 231 283 1,637
300 786 205 199 192 255 1,637
500 852 216 183 173 213 1,637
1000 981 196 163 136 161 1,637
2000 1,059 197 155 111 115 1,637
5000 1,13 196 141 88 82 1,637
8000 1,183 185 122 77 70 1,637
10000 1,232 161 120 59 65 1,637
15000 1,248 151 115 59 64 1,637
Total 13,055 2,484 2,329 3,469 4,855 26,192
Table 4-2. Statistics of WTP Responses: Percentage of the Whole Sample
Definitely Probably Probably Definitely
Price not not Not sure yes yes Total
0 26.084 4.765 5.437 18.509 45.205 100
10 29.322 5.559 5.742 23.152 36.225 100
20 31.643 5.681 6.414 21.808 34.453 100
40 33.293 6.109 8.125 21.564 30.910 100
60 35.553 7.208 9.102 21.197 26.940 100
90 37.752 8.552 9.896 20.098 23.702 100
150 41.662 10.324 11.973 16.799 19.243 100
200 44.716 11.484 12.401 14.111 17.288 100
300 48.015 12.523 12.156 11.729 15.577 100
500 52.046 13.195 11.179 10.568 13.012 100
1000 59.927 11.973 9.957 8.308 9.835 100
2000 64.692 12.034 9.469 6.781 7.025 100
5000 6.903 11.973 8.613 5.376 5.009 100
8000 72.266 11.301 7.453 4.704 4.276 100
10000 75.260 9.835 7.330 3.604 3.971 100
15000 76.237 9.224 7.025 3.604 3.910 100
Total 49.843 9.484 8.892 13.245 18.536 100
26
Table 5-1. Statistics of WTP Responses with Normal Demand: Frequency
Definitely Probably Probably Definitely
not not Not sure yes yes Total
0 0 0 0 249 589 838
10 41 11 14 320 452 838
20 71 15 29 297 426 838
40 92 27 56 291 372 838
60 120 49 76 278 315 838
90 153 70 89 262 264 838
150 205 100 127 213 193 838
200 251 121 133 170 163 838
300 297 142 128 135 136 838
500 358 158 110 113 99 838
1000 477 145 84 71 61 838
2000 553 145 71 43 26 838
5000 621 145 46 19 7 838
8000 672 136 19 9 2 838
10000 720 113 4 1 0 838
15000 735 103 0 0 0 838
Total 5366 1480 986 2471 3105 13408
Table 5-2. Statistics of WTP Responses with Normal Demand: Percentage
Definitely Probably Probably Definitely
not not Not sure yes yes Total
0 0.000 0.000 0.000 29.714 70.286 100
10 4.893 1.313 1.671 38.186 53.938 100
20 8.473 1.790 3.461 35.442 50.835 100
40 10.979 3.222 6.683 34.726 44.391 100
60 14.320 5.847 9.069 33.174 37.589 100
90 18.258 8.353 10.621 31.265 31.504 100
150 24.463 11.933 15.155 25.418 23.031 100
200 29.952 14.439 15.871 20.286 19.451 100
300 35.442 16.945 15.274 16.110 16.229 100
500 42.721 18.854 13.126 13.484 11.814 100
1000 56.921 17.303 10.024 8.473 7.279 100
2000 65.990 17.303 8.473 5.131 3.103 100
5000 74.105 17.303 5.489 2.267 0.835 100
8000 80.191 16.229 2.267 1.074 0.239 100
10000 85.919 13.484 0.477 0.119 0.000 100
15000 87.709 12.291 0.000 0.000 0.000 100
Total 40.021 11.038 7.354 18.429 23.158 100
27
Table 6-1. Distribution of the Estimated WTP with Normal Demand
Variable Obs Percentile Centile [95% Conf. Interval]
Wtp 835 0 0.269 0.269 0.269
10 11.326 6.776 15.400
20 39.322 31.794 46.897
30 69.673 60.000 84.881
40 120.869 97.512 130.716
Mean : 758.8494 50 171.544 150.103 200.253
Stand. Err. 1586.139 60 255.959 221.416 312.481
70 468.126 398.388 549.162
80 879.748 746.574 1147.648
90 2108.107 1793.560 2488.585
100 11872.180 11872.180 11872.18
Table 6-2. Average Value of Risk Reduction by Sex
Variable Sex Obs Mean Std. Dev. Min Max
Morbidity Male 576 856,576.3 2168075 131.2368 2.20e+07
Female 249 954,089.4 1865910 438.253 1.42e+07
Mortality Male 576 1,725,847 4212262 203.2255 3.45e+07
Female 249 2,519,660 4948185 753.1705 3.70e+07
Table 6-3. Average Value of Risk Reduction by Age
Variable Sex age Obs Mean Std. Dev. Min Max
Morbidity Male 15-44 415 1,131,665 2495159 517.131 2.20e+07
45-54 116 179,377 325070.7 217.702 2287034
55-64 36 71,487 102289 131.2368 388329.4
65-74 8 45,707 60048.31 216.3856 147747.7
75+ 1 180 . 180.0348 180.0348
Female 15-44 213 1,062,087 1984652 1633.342 1.42e+07
45-54 30 326,019 609848.5 438.253 2803215
55-64 5 278,312 319122.8 37641.95 662462.8
65-74 1 171,591 . 171591.3 171591.3
75+ 0 . . . .
Mortality Male 15-44 415 2,302,021 4831718 825.3475 3.45e+07
45-54 116 298,932 605489.8 414.5512 4355004
55-64 36 99,493 146848.8 203.2255 601343.5
65-74 8 61,381 78463.8 336.9885 194385.4
75+ 1 247 . 247.2682 247.2682
Female 15-44 213 2,854,431 5264090 4593.689 3.70e+07
45-54 30 545,312 1031117 753.1705 4817534
55-64 5 531,069 620468 59732 1260051
65-74 1 386,661 . 386661.3 386661.3
75+ 0 . . . .
28
Table 7. Determinants of WTP with Normal Demand
(Robust Regression on Log (Mean WTP)
Variables Coefficients
worker -0.094
(0.66)
married -0.011
(0.06)
smoking -0.190
(1.26)
Log(income) 0.418
(3.99)***
education 0.621
(2.26)**
Rcancer 0.355
(1.42)
Yuncertain -0.385
(1.71)*
Healthcheck 0.292
(2.02)**
religion 0.023
(0.10)
trust 0.339
(2.38)**
need 0.187
(2.05)**
Region-, age- and sex- Guizhou
specific dummies Tianjin Jiangsu
age15_44_male -0.007 Reference 0.886
(0.03) -- (3.98)**
age45_55_male 0.464 -0.087 0.686
(1.71) (0.18) (2.39)**
age55_65_male -0.294 0.123 0.045
(0.54) (0.14) (0.07)
age65plus_male -1.774 No Obs. 1.830
(2.10)** -- (2.06)**
age15_44_female -0.205 0.119 0.158
(0.77) (0.47) (0.42)
age45_55_female 0.085 No Obs. 0.264
(0.17) -- (0.32)
age55plus_female 1.578 2.296 -0.666
(2.64)*** (3.10)*** (2.23)**
Constant -0.688
(0.69)
Observations 816
R-squared 0.12
Robust t statistics in parentheses, * significant at 10%, ** significant at 5%; *** significant at
1%
29
Table 8. Average Value of Risk Reduction Based on Projected WTP
Normal Extremely Normal+high Whole
demand high demand demand sample
Mean WTP 439.4 546.0 460.2 411.7
Projected (Yuan)
Mean cancer 15.5 14.3 15.3 15.7
morbidity (1/10000)
Mean cancer 9.3 8.2 9.1 9.5
mortality (1/10000)
Average Value of 283,273 382,548 301,424 261,446
morbidity (Yuan)
Average value of 471,442 664,767 505,530 431,596
mortality (Yuan)
Table 9-1: WTP Function of Cancer Morbidity Risk Reduction
Model Model 6
(Dependent Model 1 Model 2 Model 3 Model 4 Model 5 Log(WTP)
Variable) (WTP) (WTP) (WTP) (WTP) (WTP)
Risk Reduction 1.705 19.808 13.939 74.795 5.990 0.023
(0.18) (0.90) (1.18) (2.21)** (0.99) (3.17)***
Risk Reduction2 -0.328 -0.782 -0.065 -0.0002
(1.06) (2.00)** (1.47) (3.18)***
risk_worker 1.319 -5.571 -0.186 -6.850
(0.23) (0.53) (0.03) (0.43)
risk_smoking -3.868 -11.533 -4.281 -15.086
(0.69) (1.31) (0.69) (1.10)
risk_fincome -0.000 -0.001 -0.000 -0.001
(1.12) (2.34)** (0.60) (1.02)
risk_education 12.669 14.230 -4.153 -36.287
(2.11)** (0.79) (0.61) (1.50)
risk_Rcancer 8.794 19.533 -10.375 -28.900
(0.97) (1.05) (0.90) (0.91)
risk_uncertainty -3.638 -8.494 4.346 18.219
(0.39) (0.60) (0.42) (0.72)
risk_health check -9.162 -7.938 -4.964 2.853
(1.80)* (0.86) (0.91) (0.20)
risk_religion 21.435 17.468 20.942 24.437
(1.54) (0.70) (1.26) (0.63)
risk_trust 7.553 20.635 -2.006 -6.548
(1.85)* (2.52)** (0.42) (0.48)
risk2_worker -0.061 0.031
(0.36) (0.16)
risk2_smoking 0.057 0.096
(0.52) (0.71)
risk2_fincome 0.000 0.000
(2.41)** (1.00)
risk2_education -0.185 0.336
(0.83) (1.32)
risk2_Rcancer -0.230 0.358
(1.09) (1.21)
risk2_uncertainty 0.221 -0.250
(1.05) (0.82)
risk2_health check 0.088 -0.078
(0.65) (0.45)
30
risk2_religion 0.104 0.140
(0.46) (0.47)
risk2_trust -0.147 0.103
(1.66)* (0.78)
Worker -227.556 -160.414 -230.357 -0.049
(1.65)* (0.91) (2.07)** (0.35)
Smoking 178.560 254.001 80.636 -0.046
(1.20) (1.35) (0.69) (0.32)
Fincome 0.008 0.012 0.005 0.304
(1.06) (1.25) (0.85) (2.91)***
Education 312.897 761.388 149.948 0.652
(1.36) (2.94)*** (0.70) (2.37)**
Rcancer 679.293 781.307 498.976 0.565
(1.95)* (1.68)* (1.87)* (2.30)**
Uncertainty -198.846 -268.940 -156.097 -0.444
(1.27) (1.20) (1.27) (1.98)**
Health check -1.315 -70.683 -70.971 0.234
(0.01) (0.40) (0.65) (1.68)*
Religion -263.355 -334.927 62.958 0.071
(1.14) (0.92) (0.28) (0.28)
Trust 430.417 454.759 401.105 0.414
(2.77)*** (2.24)** (3.37)*** (2.93)***
Constant -518.225 -1,144.424 -252.289 0.504
(1.28) (2.32)** (0.85) (0.51)
Observations 833 833 833 833 833 833
Log-likelihood -7363.41 -7340.67 -7300.07 -7296.83 -7304.22 -1745.13
R-squared -0.12 -0.07 0.03 0.02 0.03 0.05
Typical person's WTP-risk coefficient
Constant 0 0 747.02 678.45 706.77 4.853
Level term 22.67 51.31 1.677 10.192 5.990 0.023
Squared term 0 -0.506 0 -0.106 -0.065 -0.0002
Marginal WTP
(Yuan) 226,700 353,138 16,770 68,410 39,351 29,208
Average WTP
(Yuan) 226,700 433,119 489,371 514,386 496,763 110,801
Robust t statistics in parentheses. significant at 15%, * significant at 10%, ** significant at 5%; *** significant at
1%.
Table 9-2: WTP Function of Cancer Mortality Risk Reduction
Model Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
(Dependent Variable) (WTP) (WTP) (WTP) (WTP) (WTP) Log(WTP)
Risk Reduction 0.777 -0.886 7.579 32.562 2.481 0.020
(0.07) (0.03) (0.59) (0.92) (0.33) (1.84)*
Risk Reduction2 -0.247 -0.321 -0.088 -0.0003
(1.86)* (0.59) (1.08) (2.02)**
risk_worker 4.511 -3.758 3.014 -0.776
(0.62) (0.19) (0.45) (0.03)
risk_smoking -4.592 -13.559 -9.048 -21.485
(0.69) (0.90) (1.43) (1.15)
risk_fincome -0.000 -0.002 -0.000 -0.001
(1.59) (2.45)** (0.99) (0.84)
risk_education 16.603 46.923 -5.069 -23.982
(2.06)** (1.77)* (0.62) (0.76)
risk_Rcancer 11.219 49.315 -10.449 -1.980
(0.95) (1.45) (0.92) (0.05)
risk_uncertainty -6.441 -21.249 9.326 42.298
(0.56) (0.63) (0.95) (0.93)
31
risk_health check -11.627 -28.990 -2.674 -10.501
(1.85)* (2.03)** (0.45) (0.58)
risk_religion 28.130 66.962 26.888 87.209
(1.53) (1.34) (1.54) (1.43)
risk_trust 10.119 36.900 0.313 6.796
(2.02)** (2.90)*** (0.06) (0.41)
risk2_worker -0.126 0.014
(0.31) (0.03)
risk2_smoking 0.061 0.155
(0.21) (0.52)
risk2_fincome 0.000 0.000
(2.63)*** (0.43)
risk2_education -1.163 0.084
(2.51)** (0.17)
risk2_Rcancer -1.084 -0.079
(1.96)* (0.12)
risk2_uncertainty 0.807 -0.503
(1.23) (0.62)
risk2_health check 0.650 0.151
(2.18)** (0.47)
risk2_religion -0.799 -0.858
(1.25) (1.18)
risk2_trust -0.346 -0.045
(0.44) (0.22)
Worker -271.764 -250.159 -241.520 -0.066
(2.07)** (1.56) (2.15)** (0.47)
Smoking 205.419 257.786 101.575 0.009
(1.50) (1.57) (0.89) (0.06)
Fincome 0.010 0.013 0.005 0.311
(1.31) (1.48) (0.93) (2.98)***
Education 224.738 482.622 98.078 0.585
(0.91) (2.37)** (0.45) (2.07)**
Rcancer 595.629 531.328 507.543 0.582
(1.90)* (1.43) (1.91)* (2.39)**
Uncertainty -224.828 -340.606 -158.991 -0.452
(1.69)* (1.85)* (1.29) (2.01)**
Health check -33.921 9.362 -67.210 0.229
(0.26) (0.06) (0.62) (1.64)*
Religion -177.525 -431.596 54.066 0.061
(0.91) (1.70)* (0.24) (0.24)
Trust 401.842 368.080 403.771 0.425
(2.82)*** (2.19)** (3.40)*** (2.99)***
Constant -330.964 -599.908 -164.013 0.602
(0.87) (1.51) (0.53) (0.61)
Observations 833 833 833 833 833 833
Log-likelihood -7378.16 -7350.87 -7099.72 -7295.66 -7304.20 -1748.22
R-squared -0.14 -0.08 0.05 0.06 0.04 0.06
Typical person's WTP-risk coefficient
Constant 0 0 785.886 738.3830 762.3307 4.9817
Level term 28.2843 81.0879 -0.9486 11.8542 2.4805 0.0199
Squared term 0 -1.2815 0 -0.2464 -0.0882 -0.0003
Marginal WTP (Yuan) 282,843 810,879 -9,486 72,616 8,366 25,787
Average WTP (Yuan) 282,843 572,023 833,824 794,692 834,589 183,385
Robust t statistics in parentheses. significant at 15%, * significant at 10%, ** significant at 5%; *** significant at 1%.
R=9,3194, WTP=180,2293,
32
Table 10. Simulation of Marginal and Average WTPs of Risk Reduction
Risk WTP Model Log WTP Model
Reduction (Model 4) (Model 6)
(1/10000) Marginal Average Marginal Agerage Value
Value (Yuan) Value (Yuan) Value (Yuan) (Yuan)
0 59,900 + 29,469 +
0.1 59,770 70,736,835 29,485 12,841,895
0.5 59,250 14,194,975 29,549 2,591,993
1 58,600 7,126,950 29,624 1,310,790
5 53,400 1,470,190 30,035 286,044
7.5 50,150 997,385 30,109 200,724
10 46,900 760,170 30,032 158,064
15 40,400 521,330 29,401 115,300
20 33,900 400,285 28,103 93,677
40 7,900 210,592 16,342 58,364
33
Table A.1 Cancer incidence rate
(per 10,000 a year, average of 1993-1997)
Age
National average Jiangsu Tianjin
ranges
Male Female Male Female Male Female
TOTAL 24.78 19.38 25.69 13.54 24.52 20.49
0_4 1.28 0.90 0.62 0.20 1.41 1.18
5_9 0.97 0.78 0.88 0.56 1.01 1.14
10_14 1.06 0.79 0.76 0.53 1.29 0.63
15_19 1.11 0.84 0.77 0.55 1.34 0.76
20_24 1.33 1.59 1.15 0.83 1.29 1.88
25_29 2.03 2.47 2.92 1.55 1.62 2.80
30_34 3.67 4.68 8.23 3.98 2.84 4.81
35_39 7.11 8.65 18.64 7.96 5.03 7.19
40_44 12.93 13.14 31.65 16.42 11.09 11.03
45_49 19.57 19.10 45.55 22.13 19.92 17.71
50_54 28.94 24.62 43.69 23.39 31.68 26.58
55_59 40.84 34.88 59.83 27.73 40.44 44.30
60_64 75.68 53.77 93.69 39.65 76.38 64.52
65_69 112.53 69.40 114.45 48.66 123.23 80.11
70_74 151.01 89.10 134.68 55.79 178.94 98.49
75_79 164.10 97.63 149.87 72.04 183.12 107.65
80_84 153.46 92.79 102.43 40.19 182.95 99.55
85 106.89 79.35 -- -- 130.89 78.41
1. Data Source : Data for Tianjin and Jiangsu come from Parkin, D.M., S.L. Whelan, J. Ferlay and H. Storm (2005).
Cancer Incidence in Five Continents, Volumes I to VIII. International Agency for Research on Cancer and the
World Health Organisation. IARC CancerBase No 7, Lyon, 2005. Website : http://www-dep.iarc.fr/
2. Data for national average are calculated by authors according to the IRAC database.
Table A.2 National average cancer mortality rate1 (per 10,000 persons)
1991 19952 2000
Age rage male female male female male female
15-44 3.12 2.00 3.26 2.00 3.29 2.13
45-54 22.32 12.62 23.49 13.19 24.3 14.14
55-64 56.23 28.33 48.97 25.41 47.7 26.30
65-74 104.27 53.10 93.18 38.10 104.89 51.58
75+ 128.24 67.84 126.99 67.29 135.39 67.39
1. the data for 1991 and 2000 come from Yang, L., DM Parkin, LD, Li, YD, Chen and F. Bray (2004): Estimation and projection of
the national profile of cancer mortality in China: 1991-2005. British Journal of Cancer (2004) 90, 2157-2166.
2. The data for year 1995 is projected by authors. We suppose a linear growth for both the cancer incidence and population between
1991 and 2000.
3. This data also used in mortality rate estimation reported in table 7.
Table A.3 Province-specific cancer incidence rate used in estimation
(per 10000 persons)
Age ranges National average Jiangsu Tianjin
Male Female Male Female Male Female
15_44 5.20 6.09 10.484 4.995 4.205 5.210
45_55 23.55 21.39 44.730 22.668 24.800 21.446
55_65 58.13 44.45 75.832 33.466 58.331 54.173
65_75 128.46 77.78 122.593 51.193 145.114 85.854
75+ 151.92 93.35 116.020 51.852 174.414 97.546
1. calculated directly by authors from the IRAC database f with a less precise age-classification.
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Table A-4 Ranges of VSL estimates by countries, 2006 USD
No. of Health Occupation Transport Environment Other Total Mean Median
studies safety
Australia 17 0.9-2.2 2.2-21.1 1.3-5.4 0.7-5.3 1.1-13.1 0.7-21.1 4.2 2.2
Austria 5 --- 1.9-9.8 --- --- 4.0-9.8 1.9-9.8 6.7 6.1
Canada 17 2.0-6.7 0.6-5.8 0.5-30.5 --- 2.7-10.8 0.5-30.5 5.4 3.7
Demark 2 --- --- 1.0-1.4 --- 4.9-6.5 1.0-6.5 3.2 3.2
Europe 1 --- --- 4 --- --- 4 4.0 4.0
France 2 --- --- 1.1-26.6 --- 3.8-5.4 1.1-26.6 8.8 8.8
Hong Kong 1 --- 2 --- --- --- 2 2.0 2.0
Japan 4 --- 11.4-15 --- --- 6.1-9.1 6.1-15.0 11.9 13.2
New Zealand 10 --- --- 0.8-15.9 --- 2.1-3.1 0.8-15.9 5.2 3.9
South Korea 6 --- 1.0-1.9 --- --- 0.5-1.0 0.5-1.9 1.2 1.1
Sweden 7 --- --- 1.6-32.7 --- 1.6-5.0 1.6-32.7 5.9 4.2
Switzerland 5 --- 7.4-10.1 1.0-1.3 --- 5.4-9.6 1.0-10.1 5.0 5.7
Taiwan 7 --- 0.2-2.2 --- --- 1.0-1.4 0.2-2.2 1.3 1.3
UK 26 --- 1.6-8.7 0.7-25.2 23.3 1.0-30.7 0.8-86.8 13.0 6.5
US 117 0.2-8.7 0.4-24.4 0.15-37.7 0.8-10.1 0.7-31.4 0.1-37.7 6.7 5.3
Multiple 17 --- 0.4-22.3 0.15-37.7 0.07-98.7 0.5-62.9 0.1-98.7 9.9 5.6
All 244 0.2-6.5 0.2-86.8 0.15-37.7 0.07-98.7 0.5-62.9 0.1-98.7 7.0 4.9
Mean --- 3 8.2 5.9 8.3 6.3 7 --- ---
Median --- 2.7 5.5 4 6 4.5 4.9 --- ---
Source: Australian Safety and Compensation Council (2008). The initial table is in Australian Dollar (2006 price). The authors have
converted the VSL value into 2006 US dollar, with the corresponding historical exchange rate 1 Australian dollar=0.742302 US dollar.
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