4-benzamido-4'-isothiocyanostilbene-2,2'-disulfonate

This study used the CVM to estimate the WTP for building a UFP monitoring and reporting system, to evaluate the economic value of UFP information. The CVM has been widely used for economic valuation of non-market goods, especially environmental goods, and consumer perception analysis (Harrison 1992 (link); Han et al. 2011 (link); Mwebaze et al. 2018 (link)). To estimate the WTP for non-market goods using the CVM, it is important to design a questionnaire that facilitates respondents’ comprehension of issues and obtains their WTP information. Generally, payment card, open-ended, and dichotomous choice (DC) formats are employed to elicit respondents’ WTP data through the CVM. In the DC format, pre-set bids are presented to the respondents with a “Yes” or “No” choice, and econometric analysis—the probit or logit model—is used to estimate the WTP. We designed the questionnaire using the DC format because of its following strengths: easy to answer, low biases, and low likelihood of estimating unreliable WTP (Hanemann 1984 (link); Oerlemans et al. 2016 (link)).
The DC format is divided into the single-bounded dichotomous choice (SBDC) that asks a single bid (Bishop and Heberlein 1979 (link)), and the double-bounded dichotomous choice (DBDC) that asks once more for double or half of the first bid, depending on the respondent’s first answer (Hanemann 1985 (link)). The SBDC is convenient because it asks each respondent only one bid; however, it has the disadvantage of being statistically inefficient. The DBDC, in contrast, has high efficiency, but one disadvantage: the responses of the first and second bids may not be consistent (Cameron and Quiggin 1994 (link); DeShazo 2002 (link)). Respondents are likely to accept or reject the second bid, regardless of their actual WTP, out of guilt for unwillingness to pay for the second bid, which is lower than the first bid, or out of repulsion that the interviewer is trying to make at least some money by offering a lower bid. To overcome SBDC’s inefficiency and DBDC’s bias, Cooper et al. (2002 (link)) suggested the one-and-one-half-bounded dichotomous choice (OOHBDC). OOHBDC divides respondents into two groups and randomly presents an initial lower bid to one group and an initial upper bid to the other group. If respondents answer “No” to the lower bid or “Yes” to the upper bid, the survey ends. However, if they answer “Yes” to the lower bid, then the upper bid is presented as the second bid, and if they answer “No” to the upper bid, then the lower bid is presented as the second bid. This study used the OOHBDC method to reduce SBDC’s inefficiency and DBDC’s bias. In the OOHBDC method, if respondents answer “No” to the lower bid or “No–No” to the upper bid, then their WTP may be zero or between zero and the lower bid. It is important to identify whether the respondent’s WTP is actually zero or between zero and the lower bid, so as to estimate their accurate WTP; we used the spike model to solve this problem (Kriström 1997 (link)). The OOHBDC spike model asks an additional question if respondents answer “No” to the lower bid or “No–No” to the upper bid: “Are you willing to pay at least KRW 1 each year for the next 5 years from the income tax paid by your household to build the UFP monitoring and reporting system?” Fig. 1 shows the structure of the OOHBDC spike format and its possible responses.Fig. 1

The structure of the OOHBDC spike format and possible responses

This study applied the utility difference model suggested by Hanemann (1984 (link)) to estimate the WTP using the OOHBDC spike model. Each respondent has the indirect utility function $\left(j,,,m,;,S\right)$ , where $j$ is the status of the UFP monitoring and reporting system: when $j$ is equal to 1, it means the UFP monitoring and reporting system is presented; otherwise $j$ is 0. $m$ is the respondent’s income, and $S$ is the vector of respondent’s socio-economic and cognition characteristics. The indirect utility function can be expressed as the observable deterministic part, $v\left(j,,,m,;,S\right)$ , and unobservable stochastic part, ${\epsilon }_j$ , as follows: $$u\left(j,,,m,;,S\right)=v\left(j,,,m,;,S\right)+{\epsilon }_j$$ where ${\epsilon }_j$ is an independently and identically distributed (i.i.d.) variable with a zero mean.
When the respondent answers “Yes” to the question “Are you willing to pay A to build the UFPs monitoring and reporting system?,” to maximize his/her utility, the probability of answering “Yes” is expressed as follows: $$\mathrm{Pr}{\{}^{″}{\mathit{yes}}^{″}=\mathrm{Pr}\{\mathrm{\Delta }v(A)\ge \eta \}\equiv F_{\eta }[\mathrm{\Delta }v(A)]$$ where $\eta$ is the difference of error terms, ${\epsilon }_0-{\epsilon }_1$ , and $F_{\eta }\left(·\right)$ is the cumulative distribution function (CDF) of $\eta$ . Meanwhile, if the WTP (denoted as $W$ ) of the respondent is greater than or equal to $A$ , the respondent will answer “Yes,” otherwise “No.” The probability that respondent answers “Yes” can also be expressed as follows: $$\mathrm{Pr}{\{}^{″}{\mathit{yes}}^{″}\}=\mathrm{Pr}\{W\ge A\}\equiv 1-G_W(A)$$ where $G_W(A)$ is CDF of $W$ . When we consider Eqs. (2) and (3) together, we can derive $1-G_W(A)\equiv F_{\eta }[\mathrm{\Delta }v(A)]$ .
We assume that $A_i$ is an initial bid presented to the respondent $i$ , and $A_i^L$ and $A_i^U$ represent lower and upper initial bids, respectively. There are eight possible outcomes in the OOHBDC spike model: $$I\left(A_i^U\right)=\left\{\begin{array}{c}\begin{array}{cc}{I}_i^Y=1\hfill & \left(r,e,s,p,o,n,d,e,n,t,s,,i,,{answers}^{″},{\mathit{yes}}^{″}\right),where{A}_i^U<W<\infty \hfill \end{array}\hfill \\ \begin{array}{cc}{I}_i^{\mathit{NY}}=1\hfill & \left(r,e,s,p,o,n,d,e,n,t,s,,i,,{answers}^{″},{\mathit{No}-\mathit{Yes}}^{″}\right),where{A}_i^L<W<A_i^U\hfill \end{array}\hfill \\ \begin{array}{c}\begin{array}{cc}{I}_i^{\mathit{NNY}}=1\hfill & \left(r,e,s,p,o,n,d,e,n,t,s,,i,,{answers}^{″},{\mathit{No}-\mathit{Yes}-No}^{″}\right),where0<W<A_i^L\hfill \end{array}\hfill \\ \begin{array}{cc}{I}_i^{\mathit{NNN}}=1\hfill & \left(r,e,s,p,o,n,d,e,n,t,s,,i,,{answers}^{″},\mathit{No},-,\mathit{No},-,{\mathit{No}}^{″}\right),whereW=0\hfill \end{array}\hfill \end{array}\hfill \end{array}\right),$$ and $$I\left(A_i^L\right)=\left\{\begin{array}{c}\begin{array}{cc}{I}_i^{\mathit{YY}}=1\hfill & (respondentsi{answers}^{″}Yes-Ye{s}^{″}),where{A}_i^U<W<\infty \hfill \end{array}\hfill \\ \begin{array}{cc}{I}_i^{\mathit{YN}}=1\hfill & \left(r,e,s,p,o,n,d,e,n,t,s,,i,,{answers}^{″},\mathit{Yes},-,{\mathit{No}}^{″}\right),where{A}_i^L<W<A_i^U\hfill \end{array}\hfill \\ \begin{array}{c}\begin{array}{cc}{I}_i^{\mathit{NY}}=1\hfill & \left(r,e,s,p,o,n,d,e,n,t,s,,i,,{answers}^{″},\mathit{No},-,{\mathit{Yes}}^{″}\right),where0<W<A_i^L\hfill \end{array}\hfill \\ \begin{array}{cc}{I}_i^{\mathit{NN}}=1\hfill & \left(r,e,s,p,o,n,d,e,n,s,,i,,{answers}^{″},\mathit{No},-,{\mathit{No}}^{″}\right),whereW=0\hfill \end{array}\hfill \end{array}\hfill \end{array}\right),$$ where the indicator function $I(·)$ has a value of 1 if the proposition is true; otherwise, it is 0. Using eight indicator functions, the log-likelihood function for the OOHBDC spike model is expressed as follows: $$\ln L=\sum _{i=1}^N\left\{\begin{array}{c}\left(I_i^Y,+,I_i^{\mathit{YY}}\right)\ln \left[1,-,G_W,\left(A_i^U\right)\right]+\left(I_i^{\mathit{YN}},+,I_i^{\mathit{NY}}\right)\ln [G_W(A_i^U)-G_W(A_i^L)]\\ +\left(I_i^{\mathit{NNY}},+,I_i^{\mathit{NY}}\right)\ln \left[G_W,\left(A_i^L\right),-,G_W,\left(0\right)\right]+\left(I_i^{\mathit{NNN}},+,I_i^{\mathit{NN}}\right)\ln [G_W(0)]\end{array}\right)$$
Assuming that the respondent’s WTP has a logistic CDF, the spike model of $G_W(A)$ with parameter $a$ , $b$ is: $$G_W\left(A\right)=\left\{\begin{array}{c}\begin{array}{cc}{[1+exp(a-bA)]}^{-1}\hfill & ifA>0\end{array}\hfill \\ \begin{array}{cc}{[1+exp(a)]}^{-1}\hfill & ifA=0\end{array}\hfill \\ \begin{array}{cc}0\hfill & ifA<0\end{array}\hfill \end{array}\right)$$
Here, the spike is defined as ${[1+\exp \left(a\right)]}^{-1}$ , and the mean WTP is calculated as $\left(\frac{1}{b}\right)\ln [1+\exp (a)]$ .