Conceptual framework

For a referendum-style CV, utilities of voting yes and no for an individual i can be represented as ${U_{iyes}}\left( {{y_i} - {t_i},\;{x_1}} \right)$ and ${U_{ino}}\left( {{y_i},\;{x_0}} \right)$ , respectively, where ${y_i}$ is income, ${t_i}$ is the bid amount (cost) of the proposed program presented in the referendum, ${x_1}$ is the new level of quantity/quality of environmental goods/services of interest after the proposed program is implemented (benefit level), and ${x_0}$ is the current level of quantity/quality of the environmental goods/service, say wetlands. It is assumed that respondents evaluate their options based on the benefit and cost levels presented in the referendum. However, if a respondent has subjective expectations/perceptions about benefit and cost levels that deviate from the levels specified by the researcher, the utility of voting yes becomes ${\tilde U_{iyes}}\left( {{y_i} - {{\tilde t}_i},\;{{\tilde x}_{i1}}} \right)$ . For such respondents, they evaluate their tradeoffs at ${\tilde t_i}$ and ${\tilde x_{i1}}$ rather than at ${t_i}$ and ${x_1}$ which implies that the preferences measured are different from what the researcher intended to measure. Therefore, there is a potential measurement error, and WTP estimates may be biased. If we assume ${t_i} \gt {\tilde t_i}$ and $\;{x_1} \lt {\tilde x_{i1}}$ are preferred (by respondents) to ${t_i} = {\tilde t_i}$ and $\;{x_1} = {\tilde x_{i1}}$ , respectively, and ${t_i} = {\tilde t_i}$ and $\;{x_1} = {\tilde x_{i1}}$ are preferred to ${t_i} \lt {\tilde t_i}$ and $\;{x_1} \gt {\tilde x_{i1}}$ , respectively, we can predict the directions of the bias as follows:

1. 1) If ${t_i} \gt {\tilde t_i}$ , ${U_{iyes}} \lt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \gt {\widetilde {WTP}_i}$ .

2. 2) If ${t_i} = {\tilde t_i}$ , ${U_{iyes}} = {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} = {\widetilde {WTP}_i}$ .

3. 3) If ${t_i} \lt {\tilde t_i}$ , ${U_{iyes}} \gt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \lt {\widetilde {WTP}_i}$ .

4. 4) If ${x_1} \gt {\tilde x_{i1}}$ , ${U_{iyes}} \gt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \lt {\widetilde {WTP}_i}$ .

5. 5) If ${x_1} = {\tilde x_{i1}}$ , ${U_{iyes}} = {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} = {\widetilde {WTP}_i}$ .

6. 6) If ${x_1} \lt {\tilde x_{i1}}$ , ${U_{iyes}} \lt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \gt {\widetilde {WTP}_i}$ .

For example, if one perceived that the actual cost would be less than what was presented ( ${t_i} \gt {\tilde t_i}$ ), the proposed scenario would be more appealing to them than what the researcher intended ( ${U_{iyes}} \lt {\tilde U_{iyes}}$ ,). If they voted yes, then the correct inference of their WTP would be ${\widetilde {WTP}_i} \ge {\tilde t_i}$ rather than $\widehat {WT{P_i}} \ge {t_i}$ . Therefore, $\widehat {WT{P_i}} \gt {\widetilde {WTP}_i}$ . Based on the assumptions above, there are two cases where the WTP estimate is unbiased (2 and 5), two cases where the WTP estimate suffers from an upward bias (1 and 6), and two cases where the WTP estimate suffers from a downward bias (3 and 4). It is worth noting that it is less likely that respondents would perceive that more wetlands would be restored than what was proposed. Therefore, it is reasonable to suspect that Case 6 is less likely to occur or the proportion of respondents in the sample who fall under Case 6 is very small. Consequently, of the three remaining biased cases, two of them are biased downwards, and only one of them is biased upwards.

Since respondents are evaluating both benefit and cost of the proposed program simultaneously to determine which vote they cast, we need to consider ${\tilde t_i}$ and ${\tilde x_i}$ together. Considering both ${\tilde t_i}$ and ${\tilde x_i}$ together, we can predict directions of the bias as follows:

1. a) If ${t_i} \gt {\tilde t_i}$ and $\;{x_1} = {\tilde x_{i1}}$ , ${U_{iyes}} \lt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \gt {\widetilde {WTP}_i}$ .

2. b) If ${t_i} \gt {\tilde t_i}$ and $\;{x_1} \lt {\tilde x_{i1}}$ , ${U_{iyes}} \lt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \gt {\widetilde {WTP}_i}$ .

3. c) If ${t_i} = {\tilde t_i}$ and $\;{x_1} \gt {\tilde x_{i1}}$ , ${U_{iyes}} \gt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \lt {\widetilde {WTP}_i}$ .

4. d) If ${t_i} = {\tilde t_i}$ and $\;{x_1} = {\tilde x_{i1}}$ , ${U_{iyes}} = {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} = {\widetilde {WTP}_i}$ .

5. e) If ${t_i} = {\tilde t_i}$ and $\;{x_1} \lt {\tilde x_{i1}}$ , ${U_{iyes}} \lt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \gt {\widetilde {WTP}_i}$ .

6. f) If ${t_i} \lt {\tilde t_i}$ and $\;{x_1} \gt {\tilde x_{i1}}$ , ${U_{iyes}} \gt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \lt {\widetilde {WTP}_i}$ .

7. g) If ${t_i} \lt {\tilde t_i}$ and $\;{x_1} = {\tilde x_{i1}}$ , ${U_{iyes}} \gt {\tilde U_{iyes}}$ , and $\widehat {WT{P_i}} \lt {\widetilde {WTP}_i}$ .

There is one case where the WTP estimate is unbiased (d), three cases where the WTP estimate is biased downwards (c, f, and g), and three cases where the WTP estimate is biased upwards (a, b, and e). In Case d, respondents evaluate the CV scenario at the benefit and cost levels specified by the researcher. In Case c, respondents evaluate the CV scenario at the cost level specified by the researcher but at a lower benefit level than what the researcher specified. In Case f, respondents not only perceive that the actual cost level would be higher but also the benefit level would be lower than what the researcher specified. Therefore, Case f is predicted to yield the lowest WTP estimate. In Case g, even though respondents evaluate the scenario at the given benefit level, they perceive that the actual amount would be higher than what is specified. Respondents in Case a perceive that the actual cost would be lower than the specified level even though they perceive that the benefit level does not deviate. Respondents in Case b are expected to yield the highest WTP estimate as not only do they perceive that the cost would be lower but also the benefit would be higher than what the scenario describes. Lastly, in Case e, respondents perceive that the actual benefit level would be higher than what the scenario describes even though the perceived cost does not deviate from the scenario. Note that if $({t_i} \gt {\tilde t_i}$ and $\;{x_1} \gt {\tilde x_{i1}})$ or $({t_i} \lt {\tilde t_i}$ and $\;{x_1} \lt {\tilde x_{i1}})$ , the presence or the direction of bias is unclear. As discussed earlier, $\;{x_1} \lt {\tilde x_{i1}}$ is less likely to occur. Therefore, it is reasonable to suspect that Cases b and e are less likely to occur, or the proportion of respondents who fall under the two cases in the sample is very small. Of the remaining four cases with a bias, three of them are biased downwards, and only one of them is biased upwards. When ${\tilde t_i}$ and ${\tilde x_i}$ are considered together, a downward bias becomes even more dominant compared to when ${\tilde t_i}$ and ${\tilde x_i}$ are considered separately. Therefore, it can be concluded that without detecting subjective perceptions about the actual benefit and cost levels and without accounting for them, WTP may be generally underestimated. This finding contrasts with the upward bias that the literature generally finds and focuses on due to the hypothetical nature of CV – hypothetical bias (e.g., Champ and Bishop Reference Champ and Bishop2001; List Reference List2001; List and Gallet Reference List and Gallet2001; Aadland and Caplan Reference Aadland and Caplan2003; Brown, Ajzen, and Hrubes Reference Brown, Ajzen and Hrubes2003; Murphy et al. Reference Murphy, Allen, Stevens and Weatherhead2005; Hensher Reference Hensher2010; Loomis Reference Loomis2011; Penn and Hu Reference Penn and Hu2019; Schmidt and Bijmolt Reference Schmidt and Bijmolt2020).

Data

Data used in this paper are from an online survey which was administered in 2020 by Qualtrics to its online panels with a goal to understand Floridians’ preferences for restoring coastal wetlands in Tampa Bay which is a large natural harbor and shallow estuary connected to the Gulf of Mexico on the west-central coast of Florida. A total of 7,483 Qualtrics panels were invited to take the survey, and 4,146 of them responded to the survey, yielding a response rate of 55.4 percent. After controlling for age, gender, race, education, and income to ensure the representativeness of the sample, 1,243 completed responses were provided by Qualtrics, yielding the incidence rate of 30 percent.

The survey instrument was largely adopted from Petrolia, Interis, and Hwang (Reference Petrolia, Interis and Hwang2014) and Interis and Petrolia (2016). The survey first provided detailed information about wetlands and ecosystem services provided by them such as wildlife habitats, fisheries support, storm surge protection, and improved water quality. The survey then provided information about how much wetlands have been lost in the area since 1900. The survey stated that policy makers are considering a project that will restore roughly 15,000 acres of wetlands back to the 1900 level. In the referendum-style valuation question, the cost of the proposed project was presented as a one-time payment that would be added to the 2021 federal income tax return. The cost was randomized from the following range: {$50, $300, $650, $950, $1,200}. The referendum question also included a budget constraint reminder and an option to opt-out (“I prefer not to vote”) as suggested by Arrow et al. (Reference Arrow, Solow, Portney, Leamer, Radner and Schumar1993). Figure 1 presents an example of the valuation question. Table 1 presents responses to the referendum at different bid levels. Overall, out of 1,243 responses, 798 voted yes (64.2 percent), 259 voted no (20.8 percent), and 186 (15.0 percent) opted out. After removing opt-out responses, 1,057 responses were used for the analysis.

Figure 1. Valuation question example.

Table 1. Cross-tabulation between vote and bid in the referendum

In order to elicit respondents’ subjective perceptions about the benefit level of the project, the following question was included in the survey:

1. 1. If implemented, the project would restore wetlands to the proposed level.

2. 2. If implemented, the project would restore wetlands but less than the proposed level.

3. 3. If implemented, the project would restore more wetlands than the proposed level.

4. 4. I don’t know.

Responses to the question are presented at the top of Table 2. About a half of the respondents (49.9 percent) perceived that the project would restore wetlands to the proposed level ( $\;{x_1} = {\tilde x_{i1}}$ ), 30.8 percent perceived that the project would restore less wetlands than what was presented ( $\;{x_1} \gt {\tilde x_{i1}}$ ), 7.3 percent perceived that the project would restore more wetlands than what was presented ( $\;{x_1} \lt {\tilde x_{i1}}$ ), and 12.1 percent reported that they were uncertain about what the actual restoration level would be. As suspected, only a small proportion of the respondents perceived that more wetlands would be restored than what was proposed. Based on responses to the question, the following dummy variables were constructed to control for the subjective perceptions about the benefit level: “less benefit” (=1 if chose 2; =0 otherwise), “more benefit” (=1 if chose 3; =0 otherwise), and “DK benefit” (=1 if chose 4; =0 otherwise). Those who chose 1 served as the reference. It is hypothesized that ${\beta _{less\;benefit}} \lt 0$ and ${\beta _{more\;benefit}} \gt 0$ .

Table 2. Perceived benefit and cost levels

In order to elicit respondents’ subjective perceptions about the cost of the project, the following question was included in the survey:

1. 1. If implemented, I would pay the amount presented in the survey.

2. 2. If implemented, the actual cost would be lower than the amount presented in the survey.

3. 3. If implemented, the actual cost would be higher than the amount presented in the survey.

4. 4. I don’t know.

Responses to the question are presented at the bottom of Table 2. Just over a third of the respondents (36.6 percent) perceived that the actual cost would be what was presented in the survey ( ${t_i} = {\tilde t_i}$ ), 25.7 percent of the respondents perceived that the actual cost would be lower than what was presented ( ${t_i} \gt {\tilde t_i}$ ), 15.4 percent of the respondents perceived that the actual cost would be higher than what was presented ( ${t_i} \lt {\tilde t_i}$ ), and 22.2 percent of the respondents stated that they were uncertain about what the actual cost would be. Based on responses to the question, the following dummy variables were constructed to control for the subjective perceptions about cost: “less pay” (=1 if chose 2; =0 otherwise), “more pay” (=1 if chose 3; =0 otherwise), and “DK pay” (=1 if chose 4; =0 otherwise). Those who chose 1 served as the reference. It is hypothesized that ${\beta _{less\;pay}} \gt 0$ and ${\beta _{more\;pay}} \lt 0$ . As for those who are uncertain about the actual benefit and cost levels, the sign of the coefficients is unclear.

Table 3 presents a cross-tabulation between the bid and perceived cost levels. The proportion of respondents who perceived that the actual cost would be what was presented in the survey ( ${t_i} = {\tilde t_i}$ ) tended to decrease as the bid amount increased, and the proportion of “DK pay” tended to increase as the bid amount increased, but there were no clear patterns. Table 4 presents a cross-tabulation between the perceived benefit and cost levels. A large proportion of the sample believed that the actual benefit and cost levels would be what was presented in the survey (Case d) which is good, but the proportion was smaller than one third (27.4 percent) which is concerning because it implies that 72.6 percent the sample is potentially biased. Also, 10.5 percent, 7.4 percent, 6.7 percent, 3.6 percent, 2.6 percent, and 1.3 percent of the sample fell under Cases a, f, c, g, b, and e, respectively. In the conceptual framework, it was suspected that the Cases b and e would be less likely to occur. Data indicate that the Cases b and e indeed had the smallest proportions amongst all cases in the sample. Data also indicate that 17.7 percent of the sample is potentially biased downwards (c, f, and g), whereas 10.5 percent of the sample is potentially biased upwards (a). Therefore, data signals that the WTP estimate is likely to be biased downwards if the subjective perceptions are not accounted for, and the assumptions that ${t_i} \gt {\tilde t_i}$ and $\;{x_1} \lt {\tilde x_{i1}}$ are preferred (by respondents) to ${t_{}} = {\tilde t_i}$ and $\;{x_1} = {\tilde x_{i1}}$ , respectively, and ${t_i} = {\tilde t_i}$ and $\;{x_1} = {\tilde x_{i1}}$ are preferred to ${t_i} \lt {\tilde t_i}$ and $\;{x_1} \gt {\tilde x_{i1}}$ , respectively, hold. Finally, it is worth noting that for 40.3 percent of the sample, the presence or the direction of a potential bias cannot be predicted (for those who are uncertain about the actual cost and benefit levels and those who fall under cases where [ ${t_i} \gt {\tilde t_i}$ and $\;{x_1} \gt {\tilde x_{i1}}$ ] or $[{t_i} \lt {\tilde t_i}$ and $\;{x_1} \lt {\tilde x_{i1}}$ ]).

Table 3. Cross-tabulation between bid and perceived cost levels

Table 4. Cross-tabulation between perceived benefit and cost levels

Note: Percentages out of 1,057 are in the parentheses.

In addition to the dummy variables designed to control for subjective perceptions about the benefit and cost levels, other demographic variables such as “income” which is the annual household income with a range from 1 (less than $9,999) to 21 ($200,000 or more) with $10,000 increments, “white” (=1 if race is white; =0 otherwise), “employed” (=1 currently employed; =0 otherwise), and “college” (=1 if holds a bachelor’s degree or higher; =0 otherwise) were included in the regression model. Table 5 presents summary statistics of the variables used in the regression analysis.

Table 5. Summary statistics

Econometric model

Following Greene (Reference Greene2012), responses to the referendum question can be modeled using the latent regression approach. A latent regression for the data can be specified as

(1) $${y^{\rm{*}}} = {\beta _0} + {\beta _1}Bid + {\boldsymbol{\beta}} _X^{'}{\boldsymbol{X}} + {\boldsymbol{\beta}} _T^{'}{\boldsymbol{T}} + {\boldsymbol{\beta}} _Z^{'}{\boldsymbol{Z}} + \varepsilon $$

where the observed counterpart to y* is y = 1 if and only if y* > 0; ${\boldsymbol{\beta}} _X^{'}$ and ${\boldsymbol{X}}$ are vectors of coefficients and the perceived benefit level variables; ${\boldsymbol{\beta}} _T^{'}$ and ${\boldsymbol{T}}$ are vectors of coefficients and the perceived cost level variables; ${\boldsymbol{\beta}} _Z^{'}$ and ${\boldsymbol{Z}}$ are vectors of coefficients and the other individual-specific variables, and $\varepsilon $ is the error term. Further, ${\boldsymbol{\beta}} _X^{'}{\boldsymbol{X}}$ , ${\boldsymbol{\beta}} _T^{'}{\boldsymbol{T}}$ , and ${\boldsymbol{\beta}} _Z^{'}{\boldsymbol{Z}}$ are specified as

(2) $${\boldsymbol{\beta}} _X^{'}{\boldsymbol{X}} = {\beta _2}LessBenefit + {\beta _3}MoreBenefit + {\beta _4}DKBenefit$$

(3) $${\boldsymbol{\beta}} _T^{'}{\boldsymbol{T}} = {\beta _5}LessPay + {\beta _6}MorePay + {\beta _7}DKPay$$

(4) $${\boldsymbol{\beta}} _Z^{'}{\boldsymbol{Z}}{\rm{\;}} = {\beta _8}Income + {\beta _9}White + {\beta _{10}}Employed + {\beta _{11}}College$$

Note that those who perceived that the actual benefit and cost levels would be what was specified in the survey serve as the base category. Assuming that $\varepsilon $ is normally distributed, it can be estimated using the probit model.

Following Haab and McConnell (Reference Haab and McConnell2002), the overall WTP is calculated as

(5) $$WT{P_{Overall}} = - { {\beta _0} + {\boldsymbol{\beta}} _X^{'}{\boldsymbol{\bar X}} + {\boldsymbol{\beta}} _T^{'}{\boldsymbol{\bar T}} + {\boldsymbol{\beta}} _Z^{'}{\boldsymbol{\bar Z}}\over{{{\beta _1}}}}$$

where ${\boldsymbol{\overline X}}$ , ${\boldsymbol{\overline T}}$ , and ${\boldsymbol{\overline Z}}$ are vectors of the variables evaluated at their means. Separate WTPs based on the benefit and cost perceptions can be calculated as

(6) $$WT{P_{{x_j},{t_k}}} = -{ {\beta _0} + {\beta _j} + {\beta _k} + {\boldsymbol{\beta}} _Z^{'}{\boldsymbol{\bar Z}}\over{{{\beta _1}}}{\rm{\;\;}}}$$

where ${\beta _j}$ is the coefficient of the corresponding perceived benefit level (j = 2, 3, 4), and ${\beta _k}$ is the coefficient of the corresponding perceived cost level (k = 5, 6, 7). For example, WTP for those who perceived that the actual benefit and cost levels would be higher than what was presented in the survey is

(7) $$WT{P_{{x_{more{\rm{\;}}benefit}},{t_{more{\rm{\;}}pay}}}} = -{ {\beta _0} + {\beta _3} + {\beta _6} + {\boldsymbol{\beta}} _Z^{'}{\boldsymbol{\bar Z}}\over{{{\beta _1}}}}$$