1. Introduction

Various preference-based methods have been developed to reveal public demand for environmental goods or services where market prices are unavailable. One of the most widely used methods is the contingent valuation method (CVM), which has been accepted in both political and academic areas (Vossler and Evans, Reference Vossler and Evans2009; Carson et al., Reference Carson, Groves and List2014; Vossler and Holladay, Reference Vossler and Holladay2018).

In microeconomics, consumers are assumed to have well-defined preferences for goods or services provided in the market, i.e., the assumption of completeness (Pindyck and Rubinfeld, Reference Pindyck and Rubinfeld2005). Following this assumption, respondents in CVM studies are assumed to be capable of expressing their preferences for the proposed good as an exact monetary value. However, empirical studies provide evidence that people generally have a high level of uncertainty about their preferences, especially in the context of environmental valuation. Some researchers believe that people can provide only a range of willingness to pay (WTP) instead of an exact amount (Wang, Reference Wang1997; Bateman et al., Reference Bateman, Cooper, Georgiou, Navrud, Poe, Ready, Riera, Ryan and Vossler2005; Hanley et al., Reference Hanley, Kriström and Shogren2009; Voltaire et al., Reference Voltaire, Pirrone and Bailly2013). While some uncertainty can be mitigated by a better survey design, some uncertainty can never be resolved (Wang, Reference Wang1997; Shaikh et al., Reference Shaikh, Sun and van Kooten2007).

Existing studies (e.g., Hanley et al., Reference Hanley, Kriström and Shogren2009; Brouwer, Reference Brouwer2011; Voltaire et al., Reference Voltaire, Pirrone and Bailly2013) have identified several determinants of valuation uncertainty, including respondents' attitudes toward contributing to public programs, their knowledge of the public good to be valued, family income, and costs. However, in different studies, researchers have focused on different factors; thus, a unified theoretical model about the determination of uncertainty has not yet emerged (Brouwer, Reference Brouwer2011), and little is known about this topic (Alberini et al., Reference Alberini, Boyle and Welsh2003; Akter et al., Reference Akter, Bennett and Akhter2008).

Moreover, there is no consensus about the ways in which people's WTP uncertainty can be measured. To obtain an individual-level uncertainty measurement, most previous analyses using the dichotomous choice WTP question format are based on self-reported numerical certainty scales (NCSs), e.g., 1–10 or 0–100 per cent, or polychotomous categories (PCs), e.g., ‘definitely yes’, ‘probably yes’, ‘not sure’, ‘probably not’ and ‘definitely not’, elicited by follow-up questions posed after dichotomous choice valuation questions. However, this ‘response uncertainty’ reveals only respondent's uncertainty at a randomly proposed specific bid price, which means that these self-reported uncertainty levels lack comparability due to their dependence on the proposed bid price. An alternative uncertainty measurement that can overcome these concerns is one that follows the approach developed by Wang and He (Reference Wang and He2011), which is based on the WTP responses collected by a multiple bounded discrete choice (MBDC) elicitation format. This valuation approach can estimate the WTP mean value and variance for each respondent; in their paper, the authors propose measuring the uncertainty of an individual by the estimated standard variance in his or her individual distribution of WTP.

To better understand these issues, we first conduct a comprehensive review of the potential determining factors of valuation uncertainty that have been previously discussed in the literature. Following this, we reclassify these factors into three categories: demand-side factors, including respondents' attitudes, knowledge or past experience with related environmental goods and personal income levels; perceived supply-side factors, such as belief in the proposed environmental good and trust level toward the institution providing it; and finally, general sociodemographic determinants. By doing so, we attempt to contribute to the related literature by proposing a theoretical framework and a global approach that allow us to analyze the potential determinants of WTP uncertainty in a comprehensive way. As a second step, based on a CVM survey using an MBDC-format WTP question that was collected in 2014 in northern China, we adopt both the individual-level uncertainty measure initially proposed by Wang and He (Reference Wang and He2011) and its alternative transformations based on related discussions from the literature (e.g., Hanley et al., Reference Hanley, Kriström and Shogren2009; Voltaire et al., Reference Voltaire, Pirrone and Bailly2013) to analyze how the identified demand-side and perceived supply-side factors affect people's valuation uncertainty. To our knowledge, this is the first study in which different uncertainty measurements and one at the individual level calculated from the Wang and He (Reference Wang and He2011) approach are compared.

The remainder of this paper is structured as follows. In section 2, we first present different determinants of valuation uncertainty previously discussed in the CVM literature, followed by the presentation of our reclassification of these determinants. Section 3 presents the different strategies for measuring respondents' valuation uncertainty currently used in CVM studies, highlighting why we prefer to adopt the approach of Wang and He (Reference Wang and He2011) in our paper. Our survey and data are introduced in section 4. In section 5, the initial and alternative measures of individuals' WTP uncertainty are introduced, followed by the development of a theoretical framework to analyze the potential determinants of valuation uncertainty. The empirical results are presented and discussed in sections 6 and 7. Conclusions and discussions are provided in section 8.

2. Literature review on identified determinants of valuation uncertainty

The CVM literature has proposed different determinants to explain often-observed respondents' valuation uncertainty.

Bid price is considered by many authors to be an important source of uncertainty identified in existing CV studies. Based on a survey of 1,600 U.S. households for Mexican Spotted Owl recovery, Loomis and Ekstrand (Reference Loomis and Ekstrand1998) reported a quadratic relationship between bid prices and payment certainty measured by a follow-up self-reported ten-point scale. This relationship implies that valuation uncertainty is lowest for very high and very low bids but increases when the intermediate-level bid is proposed. A similar quadratic relationship between bid prices and uncertainty was also revealed in Brouwer (Reference Brouwer2011), which presents a study on the valuation of water quality improvement in the Scheldt River basin using a self-reported percentage certainty scale. However, other studies have reported different patterns for the relationship between uncertainty and proposed bid price. For example, in a study on people's WTP for a whale conservation program, Lyssenko and Martínez-Espiñeira (Reference Lyssenko and Martinez-Espineira2012) estimated an ordered logit model with the ten-point certainty scale as the dependent variable. They found a negative correlation only between bid price and uncertainty; more precisely, the higher the bid price is, the lower the response certainty is. A similar finding was also reported by Akter et al. (Reference Akter, Brouwer, Brander and Van Beukering2009), who studied air travelers' WTP for carbon offsets with five options for verbal categories as an uncertainty measure.

Respondents' attitudes toward the good being valued are also often reported to be significantly correlated with uncertainty in valuation answers. The literature shows that respondents who are in favor of environmental protection programs (Champ and Bishop, Reference Champ and Bishop2001), those who believe that the environment should be protected irrespective of the costs and who have a greater sense of responsibility for contributing to mitigating climate change (Akter et al., Reference Akter, Brouwer, Brander and Van Beukering2009) and those who have a positive attitude toward contributing to nature conservation actions (Voltaire et al., Reference Voltaire, Pirrone and Bailly2013) are more inclined to provide more certain WTP responses. On the other hand, Samnaliev et al. (Reference Samnaliev, Stevens and More2006) found that respondents who object to user fees are also more certain of rejecting the proposed bid price. In a valuation study of coastal water quality improvement in Scotland, Hanley et al. (Reference Hanley, Kriström and Shogren2009) reported that the more interesting an individual finds the interview, the greater their valuation uncertainty is.

The impacts of knowledge of or experiences with valued public goods are considered in many studies, and the findings are generally consistent. Prior knowledge was found to reduce uncertainty in Loomis and Ekstrand (Reference Loomis and Ekstrand1998), Hanley et al. (Reference Hanley, Kriström and Shogren2009) and Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013). Champ and Bishop (Reference Champ and Bishop2001) reported that respondents with more experience in donating money to environmental causes generally have lower levels of valuation uncertainty. Brouwer (Reference Brouwer2011) also found that familiarity with valuation scenarios reduces response uncertainty.

Although no consistent conclusions have been revealed, the discussion about the impacts of trust-related factors on valuation uncertainty should not be neglected. Brouwer (Reference Brouwer2011) found that people who do not believe in the reasonable utilization of funds and lack trust in the organization providing environmental goods tend to be more certain about their WTP for water quality improvement. In contrast, in Akter et al. (Reference Akter, Brouwer, Brander and Van Beukering2009), respondents' belief in the effectiveness of the proposed program was found to reduce the uncertainty of WTP for carbon offsets.

Basic socioeconomic and demographic characteristics are also considered to be correlated with valuation uncertainty in CVM studies, although less consistent conclusions can be drawn. Brouwer (Reference Brouwer2011) and Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013) suggested that the higher the income level is, the more certain the respondents are about their WTPs, while higher household income seems to increase the level of valuation uncertainty according to Hanley et al. (Reference Hanley, Kriström and Shogren2009). Gender and age are also identified as significant determinants of uncertainty. Lyssenko and Martínez-Espiñeira (Reference Lyssenko and Martinez-Espineira2012) reported that males tend to be less certain about their WTP responses; however, opposite conclusions were found in Mahieu et al. (Reference Mahieu, Riera and Giergiczny2012) and Brouwer (Reference Brouwer2011). In Brouwer (Reference Brouwer2011), younger people were found to be more certain, while in Mahieu et al. (Reference Mahieu, Riera and Giergiczny2012) and Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013), older people were found to be more certain.

As presented above, although various determinants of uncertainty have been considered by researchers, there is not yet a clear consensus across studies; the same factor can be found to play quite different roles in different studies. We did not find any study that has analyzed the relative importance of these factors in uncertainty determination. Although it is impossible to develop a vector that includes all the factors considered in past studies, a comprehensive analysis of potential determinants of valuation uncertainty is needed for a better understanding of this issue. In this article, we propose to classify the major determinants of uncertainty identified in the CVM literature, except for some basic demographic characteristics (e.g., gender, age, education, income), into either the demand side or the perceived supply side. Determinants of uncertainty on the demand side can be defined as the factors that affect an individual's perception of the benefits that they can obtain from the valued good, e.g., previous visiting experiences at similar sites (Hanley et al., Reference Hanley, Kriström and Shogren2009) and the general belief that natural resources should be protected (Akter et al., Reference Akter, Brouwer, Brander and Van Beukering2009). In addition, as income is an important determinant of respondents' demand for the valued good in the CVM literature, we also consider future income uncertainty to be an important determinant of valuation uncertainty on the demand side.Footnote ¹ On the supply side, uncertainty determinants mainly refer to whether an individual trusts the government to supply the proposed good or believes in the promised effects. In other words, supply-related uncertainty determinants describe, from the perspective of respondents, the extent to which a valued public good is provided at its promised level. In table 1 which cites the related literature, we provide detailed information on the two sides of uncertainty determinants, as well as basic demographic characteristics identified in the existing studies.

Table 1. Reclassification of uncertainty determinants identified in previous studies

3. Literature review on measurement of uncertainty

Analyzing the determinants of valuation uncertainty necessitates a discussion of the existing measurements of uncertainty. Previous studies can be classified into two major groups according to the valuation uncertainty measures adopted.

In the first group, after the WTP questions, respondents' uncertainty is measured by a follow-up question that most often employs a self-rated certainty scale asking how certain the respondents are about their WTP answers. Such a scale can either be numerical (the NCS method) or verbal polychotomous (the PC method). A ten-point scale (expressed as 1–10, with 1 indicating very uncertain and 10 indicating very certain) is most widely used when the NCS method is adopted (Loomis and Ekstrand, Reference Loomis and Ekstrand1998; Champ and Bishop, Reference Champ and Bishop2001; Samnaliev et al., Reference Samnaliev, Stevens and More2006; Lyssenko and Martínez-Espiñeira, Reference Lyssenko and Martinez-Espineira2012). Similarly, a self-reported percentage certainty scale (0–100 per cent, with 0 per cent indicating very uncertain and 100 per cent indicating very certain) has also been adopted by some researchers (Brouwer, Reference Brouwer2011). Other researchers have used verbal categories (e.g., extremely unlikely, fairly unlikely, not sure, fairly likely, extremely likely) as uncertainty measures (Akter et al., Reference Akter, Brouwer, Brander and Van Beukering2009). We also find studies that have adopted graphical/visual illustrations for respondents' uncertainty levels, such as Corso et al. (Reference Corso, Hammitt and Graham2001) and Krupnick et al. (Reference Krupnick, Alberini, Cropper, Simon, O'Brien, Goeree and Heintzelman2002).

For both the NCS and PC methods, two fundamental conditions must hold so that uncertainty information can be effectively collected (Loomis and Ekstrand, Reference Loomis and Ekstrand1998). The first condition requires respondents to be able to accurately assess their own degree of uncertainty (scored by a specific number) in their answers to the WTP questions. We, however, believe this could be a daunting task in itself, to which respondents may well introduce additional errors of their own. The second condition requires all respondents to interpret the scales equivalently. However, there might be heterogeneity in people's understanding of these scales – i.e., certain individuals tend to be systematically low or high raters (MacKenzie, Reference MacKenzie1993; Roe et al., Reference Roe, Boyle and Teisl1996) – and such incomparability of rating responses across individuals may add more noise than signals. Although some researchers believe that the PC method employing a verbal category (e.g., extremely likely or fairly likely) may lead to less heterogeneous bias, the findings of Hanley et al. (Reference Hanley, Kriström and Shogren2009) revealed that these verbal categories could still be interpreted differently by different respondents.

Another concern related to the follow-up self-rated uncertainty scale is that the follow-up uncertainty question is most frequently used after some close-ended dichotomous choice WTP questions, for which a respondent receives one bid price that the surveyor randomly chooses from a list of prices. Under these circumstances, the reported uncertainty of a respondent is therefore directly related to the bid price that he or she faces. For example, a systematically higher level of response uncertainty can be expected when the proposed bid is closer to an individual's real WTP, while lower uncertainties may be obtained when bid prices are much higher or lower than his or her real WTP.

Instead of viewing the individual's WTP as a specific value, several researchers have suggested that the individual's WTP be characterized as a random variable with a particular distribution considering valuation uncertainty (Wang, Reference Wang1997; Evans et al., Reference Evans, Flores and Boyle2003; Vossler et al., Reference Vossler, Ethier, Poe and Welsh2003; Wang and He, Reference Wang and He2011) or an interval (Hanley et al., Reference Hanley, Kriström and Shogren2009; Mahieu et al., Reference Mahieu, Riera and Giergiczny2012; Voltaire et al., Reference Voltaire, Pirrone and Bailly2013); thus, they have proposed deriving respondents' uncertainty directly from their given answers for each of the bid prices proposed in a bid price ladder/payment card. More precisely, Laplante et al. (Reference Laplante, Wang, Wu and Meisner2004), Wang et al. (Reference Wang, Laplante, Wu and Meisner2004) and Wang and He (Reference Wang and He2011) proposed the use of the MBDC or stochastic payment card (SPC) elicitation technique to invite people to reveal their payment certainty as a percentage for each of the proposed prices. The series of responses obtained from the MBDC matrix for the same person are subsequently used to separately estimate that person's individual WTP distribution. This process consists of estimating the value of the mean WTP and the variance in the WTP in a respondent-by-respondent manner, where the variance in the WTP measuring the width of the individual WTP distribution is considered by Wang and He (Reference Wang and He2011) to be an intrinsic measurement of uncertainty for this person. Relatedly, Hanley et al. (Reference Hanley, Kriström and Shogren2009) and Mahieu et al. (Reference Mahieu, Riera and Giergiczny2012) proposed using a two-way payment ladder to ask respondents to identify the bids that they are definitely willing to pay and the bids that they are definitely not willing to pay. By doing so, the intermediate bids that are left empty on the payment ladder can be used to measure respondents' uncertainty; thus, more bids left empty logically signifies a higher level of uncertainty. Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013) presented two identical price ladders to respondents and asked them to use one ladder to point out the highest price below which they would definitely pay and use the other to point out the lowest amount above which they would definitely not pay. If the amounts pointed out on the two ladders are the same, then the individual is considered to know with certainty his or her WTP; otherwise, the individual's uncertainty can be measured by the ratio of the interval formed by these two prices to the larger number of the two.

In our paper, we follow the second group of authors and consider individual WTP as a random variable where uncertainty can be measured by an interval of WTP. More precisely, in the present study, we adopt the approach of Wang and He (Reference Wang and He2011) to first reproduce their uncertainty measurement, i.e., the variance in WTP. In addition, we propose two uncertainty measurement transformations inspired by the discussions of Hanley et al. (Reference Hanley, Kriström and Shogren2009) and Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013) for comparison and robustness checks of our results.

4. Survey and data

This paper is based on a survey that was conducted in 2014 through face-to-face interviews to evaluate people's WTP for air quality improvement in Xingtai city, Hebei Province, China. In Xingtai, air pollution was among the worst in the country, and most residents strongly complained about serious air pollution but also desired rapid economic development.

Prior to the formal survey, several focus group discussions were organized during which the project team consulted with various local community workers, government officers and local residents. Discussions were held focusing on people's perceptions and attitudes toward the current local economic and environmental situation and about new air quality improvement programs. The questionnaires were developed and finalized after several rounds of pretests within the communities.

The final version of the questionnaire included four parts. In the first part, multiple questions were asked about respondents' knowledge of the health impacts of air pollution and the current air pollution control measures, as well as their subjective perceptions about the effectiveness of existing policies about environmental issues in their city (e.g., whether a respondent is satisfied with these policies enacted by the government). Respondents were also asked whether they trust the government with regard to implementing air pollution control measures. These questions were carefully designed and asked; an individual's demand-related and perceived supply-related uncertainty determinant indicators were constructed based on the provided answers. The second part queried respondents about their degree of exposure to air pollution in their daily life (e.g., whether their windows are often open), illness experiences caused by air pollution (e.g., whether they have chronic respiratory or cardiovascular diseases) and personal measures taken against air pollution (e.g., whether they wear masks and have air filters installed at home). Questions about whether respondents pay attention to green labels when shopping and about their experiences related to taking part in environmental protection activities were also asked. We expected the responses in this part to provide some objective information explaining the subjective perception indicators elicited in the first part.

The third part of the questionnaire included the valuation scenario and WTP questions. The local air quality situation was first described, and respondents were then asked about their familiarity with that information. Then, a new air quality improvement program was presented, and the respondents were told that the program implementation needed to be assured by a municipal tax at the household level, which would be collected through monthly water bills over the course of three years (i.e., from 1 January 2015 to 31 December 2017). We adopted a ‘cheap talk’ strategy to remind respondents of their budgetary constraints and the nature of the referendum applied to the final decision. This scenario was followed by the MBDC questions on WTP. More details about the valuation scenario and the MBDC matrix are provided in online appendix A. The fourth part of our questionnaire asked about people's socioeconomic and demographic characteristics. Specifically, in addition to their family income in 2013, respondents were also asked whether they had a clear picture of any potential change in their family income for the coming year.

The MBDC format was adopted for the development of valuation uncertainty measurements, in which individuals were invited to choose the possibility of voting for the implementation of the new program at each of the 18 payment levels varying from zero yuan to 1,000 yuan/month. This MBDC format has been previously used by many researchers, such as Welsh and Poe (Reference Welsh and Poe1998), Alberini et al. (Reference Alberini, Boyle and Welsh2003), Kobayashi et al. (Reference Kobayashi, Moeltner and Rollins2012), Wang and He (Reference Wang and He2011, Reference Wang and He2018) and Wang et al. (Reference Wang, Shi, Kim and Kamata2015). The design of bid levels in our study was enlightened by previous studies conducted in China, such as Wang et al. (Reference Wang, Shi, Kim and Kamata2015) and Wang and He (Reference Wang and He2018). To help reduce the cognitive burden as much as possible, inspired by Hanley et al. (Reference Hanley, Kriström and Shogren2009), Mahieu et al. (Reference Mahieu, Riera and Giergiczny2012) and Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013), in the interviews, we invited respondents to first consider the maximum amount below which they would definitely pay (the lower bound) and the minimum amount above which they would definitely not pay (the upper bound); then, they were instructed to make a choice from ‘Probably yes’, ‘Not sure’ and ‘Probably not’ for each of the bids situated between the lower and upper bounds.

To obtain relatively good geographical and socioeconomic representativeness, three districts in Xingtai city were first randomly selected; then, we selected a total of 28 communities from districts that roughly evenly covered the urban areas. One community worker from each selected community was trained to help conduct the survey by assisting with the distribution and collection of the questionnaires from the sampled households. A total of 700 questionnaires were evenly distributed among the selected communities. Households were randomly selected from each community based on the household list provided by the community office, from which vacant households were excluded beforehand. The heads of the selected households were invited to answer the questionnaire. In general, after the survey and valuation questions were introduced to the respondents, the questionnaires were left at the selected households for their response in their spare time. The community workers came two days later to collect the completed questionnaire. The neutrality and anonymity of all survey participants were ensured to the greatest extent possible. A total of 581 completed questionnaires were ultimately obtained. The questionnaires that were not included in the sample were either those not returned due to the absence of household members on the day of questionnaire collection or those for which the series of key questions were not completely answered.

5. The uncertainty measure, model and hypotheses

5.2 Model and hypotheses

Next, we use the promised air quality improvement program as the main vehicleFootnote ² to discuss how determinants of the demand and perceived supply sides affect an individual's valuation uncertainty for better air quality. Assume that an individual i's utility function at the status quo level ${E_0}$ can be written as

(1)\begin{equation}{V_{i,0}} = V\textrm{\{ }{H_i}({E_0}\textrm{)},\; {Y_{i,0}},{S_i}\} ,\end{equation}

where ${H_i}({E_0})\; \;$is the health status related to current air quality$\; {E_0}$; S_i is a vector of stable socioeconomic and demographic variables, e.g., age, education and sex; and ${Y_{i,0}}\;$is the current family income for respondent i. All the determinants are known at the current status; thus, there is no uncertainty for individual i's utility ${V_{i,0}}$.

With the proposed improvement in air quality from ${E_0}$ to ${E_1}$, all else being equal, the individual's utility becomes

(2)\begin{equation}{V_{i,1}} = V\{ {\varphi _i}[{{H_i}({E_1}} ),\; {Y_{i,1}}],\; {S_i}\} .\end{equation}

Although most of the socioeconomic variables (e.g., gender, age) are stable, we should consider the potential variation in future income since the project will be realized at some time in the future. Here, we assume that individual i has intrinsic uncertainty about the valuation of the promised air quality improvement, mainly due to uncertainty about his or her future health situation$\; H({E_1})$ and about his or her expected future income ${Y_{i,1}}$, which are captured by the random term ${\varphi _i}[{{H_i}({E_1}} ),{Y_{i,1}}].$

The individual's WTP for this improvement can therefore be written as

(3)\begin{equation}\textrm{WT}{\textrm{P}_i} = \textrm{WTP}\{{\; {H_i}({E_0}),\; {Y_{i,0}},\; {\varphi_i}[{\; {H_i}({E_1}} ),\; {Y_{i,1}}],\;{S_i}\;} \}.\end{equation}

In equation (3), ${H_i}({{E_0}} )$ and ${Y_{i,0}}$, which represent current health status and current income respectively, are frequently discussed determinants of individuals' WTP. The uncertainty term ${\varphi _i}[{\; {H_i}({E_1}} ),\; {Y_{i,1}}]$ captures the influence of the main uncertainty determinants on individual i's WTP distribution. More precisely, we expect that the greater the uncertainty term is, the greater the variance in the WTP distribution of individual i will be. Equation (3) also reminds us that if the uncertainty term ${\varphi _i}[{\; {H_i}({E_1}} ),\; {Y_{i,1}}]$ is not included in the WTP function, then its omission can cause estimation bias related to endogeneity problems.

Following the discussion in section 2, the function of an individual's valuation uncertainty, determined by the encompassing term ${\varphi _i}[{\; {H_i}({E_1}} ),\; {Y_{i,1}}]$, can be then specified as

(4)\begin{equation}\textrm{WTP}\;\textrm{uncertainty} = f\{ {\varphi _i}[{\; {H_i}({E_1}} ),\; {Y_{i,1}}]\} + \; {\epsilon _i} = f({{D_i},\;P{S_i},\;Ot{h_i}} )+ {\epsilon _i}.\end{equation}

Equation (4) assumes that people's valuation uncertainty has three categories of determinants, i.e., demand-related determinants (D), perceived supply-related determinants (PS), and other determinants (Oth), including the generally considered sociodemographic variables in the literature and extended variables concerning people's environmental attitudes and health status. $\boldsymbol{\epsilon}_{i}$ represents the error term.

The demand-related determinants (D) are factors that affect people's perceived benefits from better air quality. The previous literature allows us to identify four variables for this category of determinants. They are respondents' knowledge about the current air quality (sq), their knowledge about the existing environmental regulation (ctrlpol), their knowledge about the potential adverse health impacts caused by air pollution (health_impt) and their uncertainty about future income change (incomf_unc). We believe that better knowledge about the first three aspects should allow individuals to have a better understanding of the potential benefits of better air quality. This is because air quality can be viewed as an ‘Experience Good’, i.e., a good about which consumers are uncertain about their preferences and learn about them with each consumption event (Nelson, Reference Nelson1970, Reference Nelson1974; Stigler and Becker, Reference Stigler and Becker1977). Such an event can be, for example, the experience of suffering from chronic respiratory disease caused by air pollution. As discussed in section 2, the literature already provides some empirical insights into the role of knowledge and experiences in reducing individuals' uncertainty in WTP (Champ and Bishop, Reference Champ and Bishop2001; Hanley et al., Reference Hanley, Kriström and Shogren2009; Brouwer, Reference Brouwer2011; Voltaire et al., Reference Voltaire, Pirrone and Bailly2013). Moreover, Czajkowski et al. (Reference Czajkowski, Hanley and LaRiviere2014) presented additional theoretical evidence for the impacts of people's experience on their more certain preferences for environmental public goods. Using a Bayesian framework, the authors developed a theoretically consistent random utility model that captures this effect by allowing the model's scale parameter to be a function of experience; they concluded that a subject's preference certainty should increase with increasing experience.

The demand for goods and services is also affected by the expectation of future income change (Mankiw, Reference Mankiw2006). This is especially true in hypothetical situations where purchase decisions and payments occur at some moments in the future. In addition, air quality is considered a luxury good to some extent, implying that the demand for this service can be more sensitive to income change than the demand for necessities. Although the influence of income level on valuation uncertainty has been tested in previous studies (Hanley et al., Reference Hanley, Kriström and Shogren2009; Brouwer, Reference Brouwer2011; Voltaire et al., Reference Voltaire, Pirrone and Bailly2013), to the best of our knowledge, the impacts of future income change have still been ignored. We assume that making purchase decisions can be more difficult for individuals whose future income changes present more uncertainty. Accordingly, a higher valuation uncertainty is expected with more uncertain income changes.Footnote ³

Perceived supply-related determinants (PS) in this paper include two variables: respondents' satisfaction with the effectiveness of existing air pollution control measures (ctrl_stsf_trust) and their trust in the government to thoroughly implement the proposed air quality improvement projects (ctrl_imple_trust). Both factors can be interpreted as public trust in the supplier of the proposed public good. The distrust in public institutions has been found to contribute to lower-level support for environmental programs (Johnson and Scicchitano, Reference Johnson and Scicchitano2000). The impacts of trust-related factors on response certainty have been previously studied, but the findings are not convergent. In a study with a PC format, Akter et al. (Reference Akter, Brouwer, Brander and Van Beukering2009) concluded that respondents who believe in the effectiveness of carbon emission offsetting programs have greater levels of response certainty. However, in another study with an NCS design, Brouwer (Reference Brouwer2011) found that individuals who distrust the government are more certain in their WTP responses.

Finally, for the socioeconomic variables, for the purposes of comparison, we first include only the most frequently used ones, including gender, age, education level and household income; additionally, some health and attitudinal variables were added to the estimation in an extended model.

Following the approach of Wang and He (Reference Wang and He2011), we estimate the WTP mean and variance for each individual in the first stage as shown in online appendix B. Then, in the second step, we regress the uncertainty measured by the estimated variance of the individual WTP distribution and its transformations on the assumed determinants, as proposed in equation (4). This approach allows us to obtain a more intrinsic measurement of uncertainty in people's WTP in the first step and to avoid the potential bias in the measurement of uncertainty that can be caused by the correlation between WTP and its uncertainty, as many other one-step approaches based on cross-sectional databases involving all respondents may have.Footnote ⁴

In table 2, we report the descriptive statistics of the variables involved in our uncertainty determination models. The initial questions in the survey are also presented in the table.

Table 2. Questions and statistics of uncertainty-related variables

6. Impacts of potential uncertainty determinants

Next, we analyze how the uncertainty level in valuation is dependent on the potential determinants identified in the previous section. For the valuation uncertainty level, the logarithmic transformation Ln(${\sigma _i}/{\mu _i}$) is adopted, which describes the percentage of WTP variance with respect to the mean value of an individual's WTP.Footnote ⁵ For comparison, we also present the results with a simple Ln(${\sigma _i}$), which is the initial uncertainty measure proposed by Wang and He (Reference Wang and He2011). The measurements $\textrm{Ln}({{U_i} - {L_i}} )$ and $\textrm{Ln}(({U_i} - {L_i})/{U_i})$ developed by Hanley et al. (Reference Hanley, Kriström and Shogren2009) and Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013) are also used in our analysis as robustness checks. After excluding potential protesters, the respondents who gave negative answers at the zero bid, positive answers at the highest bid, or missing or disordered answers, we retain 426 observations for the following analysis.Footnote ⁶

Table 3 first reports the OLS estimations of the determination of valuation uncertainty, with only the most conventional sociodemographic variables included in the first four columns (Models 1–4), and both the conventional and extended sociodemographic variables (i.e., some attitudinal and health-related variables) included in the 5th to 8th columns (Models 5–8). Our results show that most of the socioeconomic and demographic characteristics included in our estimations are significant. Male respondents are found to have a significantly higher level of valuation uncertainty than women. This result can be explained by psychological studies suggesting that females tend to adopt more inclusive or rational decision modes (Blais and Weber, Reference Blais and Weber2001) and to process information in a more complex and systematic way than men (Weber et al., Reference Weber, BoÈckenholt, Hilton and Wallace2000; Mahieu, Reference Mahieu2010). These behavioral differences may lead to differences in uncertainty between males and females when assessing their WTP scenarios. We also find that older respondents have a significantly higher level of uncertainty. This can be explained by Ye et al. (Reference Ye, Li, Zhang and Zhu2010), who assumed that older people may have less access to environmental protection publicity in China. The positive impacts of education on valuation uncertainty revealed in this study are inconsistent with the findings of several past studies, such as Fischer and Hanley (Reference Fischer and Hanley2007), who found that more educated respondents more easily choose the cognitively controlled decision-making styles, which can contribute to reducing their level of uncertainty. We find only that respondents with children under 15 years old in their family have a significantly lower uncertainty degree in the models with $\textrm{Ln}(({U_i} - {L_i})/{U_i})$ as the uncertainty measure; the coefficients of this variable in the other models are not different from zero. Family income is found to significantly affect people's valuation uncertainty; however, the direction of its effect on uncertainty changes between models with different uncertainty measures. A positive impact is found when uncertainty is measured by $\textrm{Ln}({\sigma _i}/{\mu _i})$, Ln(${\sigma _i}$) or $\textrm{Ln}({{U_i} - {L_i}} )$, which is similar to the conclusions drawn in Hanley et al. (Reference Hanley, Kriström and Shogren2009), while a negative impact is found with the uncertainty measure $\textrm{Ln}(({U_i} - {L_i})/{U_i})$, which is consistent with the findings of Voltaire et al. (Reference Voltaire, Pirrone and Bailly2013). The further inclusion of variables capturing people's attitudes toward environmental protection and two variables measuring people's health increases the explanatory power of our model (cf. R ² values). Respondents declaring that they pay attention to green labels while shopping were found to have significantly higher valuation uncertainty. Having health problems themselves was found to reduce the level of valuation uncertainty (only significant for the measure $\textrm{Ln}({\sigma _i}/{\mu _i})$), while having sick family members was found to increase the level of valuation uncertainty (only significant for $\textrm{Ln}({\sigma _i}/{\mu _i})$ and $\textrm{Ln}(({U_i} - {L_i})/{U_i})$).

Table 3. Results of models with only sociodemographic variables

Note: Robust standard errors in parentheses.

Based on the estimations shown in table 3, we further add the demand-side and perceived supply-side determinants to our estimation. These new results are reported in table 4. Considering the potentially strong correlation between the demand-side and perceived supply-side determinants, which are all subjective-perception-based, we include the identified uncertainty determinants separately in six different estimations to avoid multilinearity. Therefore, the purpose of these estimations is to explore whether it is necessary to include these subjective-perception-based determinants in the uncertainty determination function but not to confirm the exact impact of each specific determinant. To save space, in table 4, we report only the coefficients of the included demand-side or perceived supply-side determinants. The coefficients of the other conventional or extended socioeconomic variables are not reported, since their value and significance remain stable in most cases. The complete estimation results can be found in online appendix D.

Table 4. Models with socioeconomic variables and uncertainty determinants

Notes: Robust standard errors in parentheses.

1. For presentation convenience, in this table, we only reported the coefficients and their robust standard errors of the separately included demand or perceived supply side uncertainty determinants. The complete estimation models always include the conventional socioeconomic variable (Models 1–4) and attitudinal and health related variables (Models 5–8). The corresponding complete estimation results can be found in online appendix D.

2. sq_know = 1: Respondents declaring ‘know a lot’ about the status quo of air quality, sq_DKmuch = 1: respondents declaring ‘don't know much’ about the status quo of air quality. The reference group is the respondents declaring ‘know nothing’ about the status quo of air quality.

3. ctrl_know = 1: Respondents declaring ‘know a lot’ about air pollution control policies, ctrl_DKmuch = 1: respondents declaring ‘don't know much’ about air pollution control policies. The reference group is the respondents declaring ‘know nothing’ about air pollution control policies.

4. health_impt_know = 1: Respondents declaring ‘know a lot’ about health impact of air pollution, health_impt_DKmuch = 1: respondents declaring ‘don't know much’ about health impact of air pollution. The reference group is the respondents declaring ‘know nothing’ about health impact of air pollution.

5. income_unc = 1: If the individuals know nothing about the change of their family income in the following year; = 0, otherwise.

6. ctrl_imple_trust = 1: If the individuals believe the government would thoroughly implement air quality improvement polices; = 0, otherwise.

ctrl_stsf_trust = 1: If the individuals are satisfied with current environmental regulation and protection measures established by the municipality; = 0, otherwise.

A comparison of the coefficients obtained for the same demand-side or perceived supply-side variable across different models reveals in general good stability; the choice of uncertainty measures and the presence of conventional or extended socioeconomic variables do not affect the stability of the results. For the role of the determinants as demand-side factors, i.e., people's knowledge about the status quo of air quality (section 1), about air pollution control policies (section 2) and about the negative health impacts of air pollution (section 3), we use the respondents who answered ‘know nothing’ as the reference group. Our estimations suggest that people's knowledge is a very important factor affecting valuation uncertainty. The results in sections 1 and 3 of table 4 show that people who do not know much about the status quo level of air quality or about air pollution's health impacts have the highest level of uncertainty in most of our models, followed by those who ‘know a lot’. Regarding knowledge about the existing control policies, as presented in section 2 of table 4, although individuals who do not know much also have the highest valuation uncertainty, there are no significant differences in the uncertainty level between people who declare that they ‘know a lot’ and those who declare that they ‘know nothing’.

The identification of respondents who reported ‘don't know much’ as having higher levels of valuation uncertainty than those who reported ‘know nothing’, although somewhat unexpected, can be explained by the following logic: people can have an opinion about their potential uncertainty regarding an issue only when they know something about it. For those who declared that they know nothing, their low level of uncertainty could be related to their low level of interest in air quality-related issues. If this is the case, we should expect these respondents to have relatively lower individual mean WTP values. To test this hypothesis, in table 5, we report the means of ${\mu _i}$ for the three groups of respondents who declared different levels of knowledge. Although the student's t tests confirm the statistical significance of the difference between groups for two of the three aspects of knowledge, the group means of individual WTP ${\mu _i}$ values demonstrate quite similar patterns in differences between groups, with people who reported knowing nothing having the lowest values, followed by people who reported not knowing much and finally those knowing a lot. The co-presence of the similarly low value of uncertainty ${\sigma _{i\; }}\;$for the group that reported knowing nothing and the one that reported knowing a lot and their mean WTP ${\mu _i}$ values standing at two extreme ends signifies the necessity of interpreting the uncertainty measures with the true intention of the respondents to either support or not support the project. Logically, these higher certainty levels reported by people who know nothing should be interpreted as negative certainty about not supporting the project. This finding echoes, to some extent, that of Hanley et al. (Reference Hanley, Kriström and Shogren2009), who showed that people with more interest but who are less informed tend to be more uncertain about their valuation than respondents with no interest.

Table 5. Student's t test for comparison of individual mean WTP and variance between groups

Note: T-values in parentheses.

Section 4 of table 4 reveals the role of future income change uncertainty, which is another potential demand-side determinant in valuation uncertainty determination. More specifically, compared to people who know something about their future income changes (income_unc = 0), those who declare that they know nothing (income_unc = 1) are reported to have a lower level of valuation uncertainty. The result remains significant in five of the eight estimations. A comparison of the mean WTP ${\mu _i}$, variance ${\sigma _{i\; }}$ and ratio ${\sigma _i}/{\mu _i}\;$ between the groups in table 5 reveals no significant differences between the groups. For those who indicated that they ‘know something’ about their future income changes, we also asked in the questionnaire about its potential trends, i.e., increases, decreases or remaining constant. The answers from the respondents show that the valuation uncertainties between people with predictions of increases, decreases and remaining constant are not significantly different but are all significantly larger than those of people who indicate that they ‘know nothing’ of their future income changes. More discussion about these results is provided in the next section.

For the supply-related determinants (cf. sections 5 and 6 of table 4), both trust in the governmental implementation of current environmental policies and the level of satisfaction with the results of the existing air pollution control measures are found to be positively correlated with the level of uncertainty in valuation.Footnote ⁷ This result echoes the findings reported in Brouwer (Reference Brouwer2011). One potential explanation is that people who do not believe in the promised implementation or who are unsatisfied with the existing policies are more certain of refusing to pay for air quality improvement. Evidence for this explanation can be found in Wang et al. (Reference Wang, He and Huang2020), who concluded that the persistence of disjuncture between governmental promises and actual performance in environmental governance has contributed to a decrease in the level of public trust and a decrease in people's WTP for new environmental regulation measures. The validity of this explanation is supported by table 5, which shows that the mean values of ${\mu _i}$ and ${\sigma _i}$ for people who declared that they do not trust in governmental implementation or are unsatisfied with existing environmental measures are much smaller than those of their counterparts. However, the differences were not confirmed by student's t tests.

A comparison of the results reported in table 4 shows that including demand-side and supply-side determinants in most cases greatly exacerbates the explanatory power of the models of valuation uncertainty determination, thereby demonstrating the necessity of including them in the determination function of valuation uncertainty. Although the increase in the R ² value seems to be sometimes greater in the models containing demand-side factors, this difference should be at least partially explained by the fact that the knowledge-related variables are captured by two dummies, while both supply-side factors are captured by only one dummy.

7. Characteristics of the respondents providing strong negative certainty

One of the common findings of table 4 is the significantly higher level of certainty found for respondents who declared that they ‘know nothing’ about benefit-related factors or their future income changes and those who do not trust or are not satisfied with the implementation of existing air pollution control measures.

To obtain a better understanding of these respondents, in table 6, we provide comparisons of the mean values of the extended list of sociodemographic characteristics between groups.

Table 6. Comparison of the sociodemographic variables between groups of respondents (student's t test)

Note: T-values in parentheses.

First, the differences in most of the conventional socioeconomic variables between groups are relatively less significant. We find significant group differences only for education and income. People who declare that they ‘know nothing’ about air quality-related knowledge are found to be significantly less educated than those who declare that they know at least something. Those who declare that they know nothing about their future income changes are also found to be less educated, and this finding is significant at the 90 per cent level. We also find that respondents who do not trust the implementation of existing air pollution control measures are also less educated than their counterparts; this outcome is also significant at the 90 per cent level. –

The extended socioeconomic variables – more precisely, the variables revealing people's attitudes toward the environment and their health conditions – seem to present more significant differences between groups. The respondents who reported knowing nothing about air pollution-related knowledge or about their future income changes, and who did not trust in or were not satisfied with the existing air quality improvement measures, are systematically found to be those who pay the least amount of attention to the green labels of goods and services that they purchase, those who participate the least in environmental protection activities, and those who systematically suffer less from health problems themselves and have the least level of concern about the health situation of their family members, all of which can be considered additional evidence about their relatively low level of interest.