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 level<sup>13</sup> . 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.

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