# 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”.<sup>11</sup> 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 (μi) 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 mortalitybased 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 yuan<sup>12</sup> . 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

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