## 3 Results and Discussion  
### Estimation Results  
The results obtained through an application of maximum likelihood estimation to the model, Equation (3), are given in Table 2. The dependent variable is the probability of responding \"yes\" to a suggested bid. As the value of the bid becomes greater, the probability should be reduced. The coefficient estimate for bid amount is negative and statistically significant at the 1% level. This is quite reasonable. Given that the sample proportion of \"no-no\" and \"no-no-no\" responses, that is, zero WTP was 37.9%, the estimated spike of 0.3859 implies that the data were well represented by the spike model. Moreover, the spike secures statistical significance at the 1% level. The Wald test can be employed for the specification test of the model. The null hypothesis is that the estimated coefficients for bid amount as well as constant terms are not distinguishable from zero. In other words, the hypothesis implies the meaninglessness of the model. The statistic was 656.28. Since this value is sufficiently large, the hypothesis could be rejected without deficiency. In addition, the \(p\)-value for the statistic was 0.000. Thus, the model possessed statistical significance. The yearly household average WTP for the reduction was obtained as KRW 5523 (USD 4.92). Uncertainties can be involved in the estimation of the average. In such cases, it may be a good idea to \begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **Coefficient Estimates (_t-Values_)** \\ \hline Constant & 0.4645 (7.31) \# \\ Bid amount a & \(-0.1724\) (\(-21.16\)) \# \\ Spike & 0.3859 (25.62) \# \\ Yearly household mean WTP & KRW 5523 (USD 4.92) \\ _t-_value & 13.70 \# \\
95\% CI b & KRW 5055 to 6076 (USD 4.90 to 5.41) \\
99\% CI b & KRW 4896 to 6284 (USD 4.36 to 5.60) \\ Sample size & 1000 \\ Log-likelihood & \(-1330.22\) \\ Wald statistic (_p-_value) c & 656.28 (0.000) \\ \hline \hline \end{tabular}  
Notes: a The unit is 1000 Korean won (USD 1.0 = 1122.8 at the time of the survey). b CI indicates confidence interval. c The null hypothesis is that all the parameter estimates are jointly zero. The # means statistical significance at the 1% level.  
\end{table} 
Table 2: Estimation results of the model and the mean willingness to pay (WTP). report confidence intervals together rather than just point estimate. To this end, this study adopted a parametric estimation technique developed by [PERSON] and [PERSON] (2006) to present a confidence interval for the average. This method assumed that the estimates of the constant term and coefficient for the bid amount, given in Table 2, followed a bivariate normal distribution and produced an empirical distribution of the mean WTP by extracting the coefficients from this distribution and calculating the mean WTP 5000 times. Cutting the appropriate proportion from the left and right sides of this empirical distribution can find 95% and 99% confidence intervals. In other words, to find 95% and 99% confidence intervals, 2.5% and 0.5% are cut from the left and right sides of the distribution, respectively. Table 2 also reports them. The results presented in Table 2 do not contain other covariates related to the interviewee's characteristics. However, other factors could influence the likelihood of reporting \"yes\" to an offered bid. For instance, some variables concerning the interviewee, such as gender, household income, and education level, can be introduced. A model including some covariates can be considered for investigating the possible effects of such variables. For this purpose, four variables were reflected in the model with covariates. Basic information about the covariates is described in Table 3.  
Table 4 shows the estimation results of the model containing the variables described in Table 3. The Wald statistic for the specification test of the model was 607.79. This indicates that the null hypothesis of the model's being meaningless was rejected, considering that its \(p\)-value became 0.000.