“A general model for treatment of protests and no-answer responses in contingent valuation method”

This study formulates a general model to account for the protest responses and no-answer replies in contingent valuation method (CVM) and should be interesting to the readers in Environmental Economics both from the methodological aspect in CVM and from the application aspect in benefit evaluation of all kinds of environmental issues and natural resources conservation. This general model is applicable to all kinds of elicitation methods in CVM. The merits of this general model are simplicity in estimation and simultaneously accounting both for protest and noanswer responses. This general model certainly can offer future CVM applications a good direction and guidance in resolving these troublesome issues in this extensive use valuation method. Creation of inverse Mills ratio is the distinctive step in this general model. The results generally indicate that these ratios are significantly different from zero. This means that accounting for these Mills ratios does have an important role in such modification when protest responses and/or no-answer responses are both taken into account. The results show that overall total WTPs from the general model with inclusion of protest and no-answer responses under different types of elicitation formats are higher than those estimated by traditional treatment. The degree of underestimation of traditional treatment is between 26% and 67%. That is, the general model proposed here for treating protest and/or no-answer responses in CVM can account for the full information which might be potentially omitted or inappropriately dealt with in the estimation.

Introduction  Contingent valuation method (CVM) is a widely used method for evaluation of non-market goods and services. All elicitation methods in the design of CVM can be classified into three groups. One is the direct revelation of willingness to pay (WTP), such as open-ended payment card, and bidding game, another is the pure discrete choice type, such as single-bounded, double-bounded, and even triplebounded, and the other is the hybrid type format For either type of elicitation method, protest responses inevitably occur for various reasons (Lindsey, 1994;Jones et al., 2008;Meyerhoff and Liebe, 2009;Meyerhoff et al., 2012). The protest responses might be identified as zero responses or could also be revealed as "no" or "no-no" replies depending upon the elicitation format. Payment vehicle, policy intervention, institutional setting, lack of comprehension of the task, insufficient information, ethical objections, or motivation to free-ride are possible causes for protest responses, which will cause the problem of sample selection bias (Atkinson et al., 2012). Without proper modification and correction, the aggregate measure of total benefits for the concerned goods and services will be biased either upwards or downwards.
Moreover, a National Oceanic and Atmospheric Administration (NOAA) expert panel (Arrow et al., 1993) suggests not pushing respondents to choose between "yes" or "no". An option of "no-answer" 1 3 should be offered in the discrete choice stage for respondents who cannot clearly make a decision between "yes" and "no" choices. Presser and Schuman (1980) also discover that number of nonresponses tends to increase if no option of "noanswer" was provided. As such, the respondent confronts three options of choices instead of two options, "yes" and "no", in the elicitation formats related to choice types. Under such circumstances, the decision tree for the analysis should be different from that when only "yes" and "no" options are provided, as in most research conducted in the past. Similarly, there are various kinds of reasons for choosing the option of "no-answer" (Alberini et al., 2003;Balcombe and Fraster, 2009;Li and Mattson, 1995;Ready et al., 2001;Shaikh et al., 2007;Wang, 1997). No matter what reasongives rise to noanswer responses, studies in the past conducted with the help of CVM rarely include "no-answer" for respondents as another option. Consequently, modification and correction for sample with such responses is hardly seen in the literature.
There are some methods to modify and/or correct the sample with protest or no-answer responses in past studies. Among these, the easiest method is to remove these types of responses. It is obvious that sample will, then, be reduced and be further biased. The inference from the estimation results will be invalidated accordingly (Jorgensen et al., 1999). Examples can be found in the studies done by Dziegielewska  Even more complicated and delicate modification and correction is estimation by a double-hurdle model (Cragg, 1971). This, then, requires Heckman's (1979) two-stage procedure to estimate the sample selection type of model. Studies doing so include Dalmau-Matarrodona (2001) and Strazzera et al. (2003). Accordingly, the full information maximum likelihood method is the most efficient method to deal with the sample selection issue (Strazzera et al., 2003). Research done by Brouwer (2012) and Fonta et al. (2010) also uses the full information maximum likelihood method to modify samples with protest responses. 4 The drawback of the full information maximum likelihood method is, however, that it is too complicated to estimate. It is normally difficult to obtain convergence in the estimation due to its nonlinearity 2 . If more information is collected from 2 Estimation of nonlinearity involves searching for the local optimization or the global optimization. Selection of good starting points of coefficients may not always fulfill the ideal location or conform to the expectation. Thus, it normally takes longer time in estimation to get convergence if it is not impossible. all the respondents, then, an alternative method, the latent class model, which treats protest responses as an attitudinal factor, is an alternative method (Zoltán, 2011). Meyerhoff and Liebe (2006; and Cunha-e-Sá et al. (2012) extend the idea of the latent class model to deal with protest responses. Other varieties of models for treating protest responses include one named multiplehurdles by Wu et al. (2004), and one named the spike model by Reiser and Shechter (1999). These methods are too complicated to achieve estimation convergence. As such, these methods are of limited usefulness in dealing with the protest responses.
As with "no-answer" responses, there are few studies which correct and modify them, because most research does not include an option of "no-answer" in the questionnaire. Even if there is an option of "noanswer" designed into the questionnaire, previous studies just remove these responses before estimation proceeds. This will cause a problem similar to protest responses. That is, the more the "no-answer" responses are removed, the more biases occur. Groothuis and Whitehead (2002), Wang (1997), and Wu et al. (2004) have designed different models to treat "no-answer" responses. Even if the focus of modification is to include responses of "no-answer", there is no general rule for how to treat these responses.
Moreover, previous studies correct or modify protest responses and no-answer responses separately. No general model, however, is appropriately employed to correct or modify protest and no-answer responses simultaneously. Thus, models for modification from previous research not only don't fully account for both protest responses and no-answer responses, but also are not suitable for all kinds of elicitation methods in CVM surveys.
Thus, construction of a general model, which is desirable and empirically applicable, is a new challenge for this field. Design of the model is not only necessary for all kinds of elicitation formats, but also essential to treat protest responses and no-answer responses concurrently. Additionally, estimation of this general model should have characteristics of higher efficiency and easier estimation than the traditional approaches. Thus, the purposes of this study are, firstly, to formulate a general model to account for the protest responses and no-answer replies for all types of elicitation methods. The model is, then, applied to a set of data from a previous study by Hung et al. (2012). Finally, the results estimated from the models constructed in this study are compared with those derived by traditional models.
The remainder of the paper is organized as follows. Section 1 constructs the general model. Section 2 is the specification of modification models. Section 3 presents the results and analyses, and final section concludes. This study intends not only to suggest a model, which is theoretically and empirically sound, but also to give a comprehensive progress record for all the models that have been developed so far for correcting protest and no-answer responses.
1. General model for non-protest, protest, and no-answer responses The general model, which modifies and corrects sample with protest and/or no-answer responses and accommodates all types of elicitation formats classified in this study, is presented in Fig. 1.
In any type of elicitation method, the first stage is to estimate the probability of each response, and to prepare its related information for WTP estimation. The second stage is, then, to estimate WTP, in which the protest and no-answer responses are all included 3 . Along such a general model, the procedure for estimation of each type of elicitation method is outlined below.
1.1. Probability estimation of each type of response. The multinomial logit stated in equation (1) is employed to estimate the probability of each response: where ij P is the probability of a designated response, i is the response and 1, 2, 3, ..., i n  , and n is the total number of responses. Additionally, j is the response type, and we assume j=1 is non-protest, j=2 is protest, and j=3 5 3 The general model constructed in this study is completely different from the idea proposed by Hsiao and Sun (1998). Their study intends to fill in missing data for certain questions or specific responses in the survey. The protest responses or don't know/uncertainty responses are is no-answer responses. The inverse Mills ratio is transformed from a multinomial logit model. There are various ways to deal with such a problem. Accordingly, Bourguignon et al. (2007) recommended that the DMF developed by Dubin and McFadden (1984) be adopted for the identified afterwards. The occurrence of potential protest responses or don't know/uncertainty responses can be determined by their corresponding probability beforehand for the model proposed in this study.

Protesters Non-protesters
No-answer

Identification of Responses by Type of Multinomial Logit
Estimation of WTP and related information for each type of elicitation format with creation of Heckman's inverse Mills ratio for the adjustment of Tobit or bivariate probit model with inclusion of non-protest, protest, and no-answer responses where MLIMRA and MLIMRF are the inverse Mills ratios calculated for non-protest and protest responses.

Estimation of WTP under each elicitation format. 1.2.1. Direct revelation of WTP format.
After estimation of probability of each response and WTP for protest responses and no-answer responses, the estimation of WTP for all responses, including protest, non-protest, and no-answer responses, can be achieved by equation (3): where E  is the coefficient to be estimated, AE  and FE  are coefficients of inverse Mills ratios from the multinomial logit model, which is used to adjust for non-protest and protest responses, respectively, under the multinomial logit model and 1 E  is the error term.

Pure discrete choice format.
Under expenditure difference interpretation, the bivariate probit model is employed to identify the differences among responses. The inverse Mills ratio generated from the multinomial logit model is, then, used as one explanatory variable structured in equation (4): The estimation of WTP from the bivariate probit model requires Heckman's inverse Mills ratio to avoid the potential sample selection bias. The Heckman inverse Mills ratio under the bivariate probit model is computed as in equation (5) below (Heckman, 1979): where μ and are the mean and variance from the bivariate probit model, and  is a constant term.
Additionally,  is the probability density function of the normal distribution for the discrete choice procedure, and  is the cumulative density function of the normal distribution in the choice process.
In order to be comparable with the results estimated from the other two categories of elicitation methods, the Tobit model is conducted for the WTP estimated from the previous stage under such condition as in equation (6): where 1 D  is the vector of coefficients to be estimated, D  is the coefficient for Heckman's inverse Mills ratio (HIMR 1 ), and is an error term. 6 4 There are various methods to estimate probability for each category of response. In order for such results to be appropriately used in further analyses to avoid potential bias, correlation between different levels of decisions has to be taken into account. The method developed by Dubin and McFadden (1984) is one such method which not only has such characteristics, but also is suitable for the data at hand.

Hybrid type format with discrete choice and open WTP revelation.
In order to account for protest responses and no-answer response for its estimation of WTP, the Heckman inverse Mills ratio (HIMR) through discrete choice for non-protest WTP estimation is included in the following Tobit model. Furthermore, it is to predict WTP for no-answer responses by using the non-protest WTP estimation. Together with all other WTP estimations, the full sample with predicted WTPs for no-answer responses and predicted WTPs for protest responses is estimated by the following equation (7): where T  is the vector of coefficients to be estimated, T  is the coefficient for Heckman's inverse Mills ratio, and 1 T  is an error term.

Traditional treatment of protest and/or noanswer responses.
To compare the results estimated from the general model developed in this study, which includes protest and no-answer responses, with those from traditional treatments of protests, estimations for the direct revelation of WTP format and for the hybrid type format with discrete choice and open WTP revelation are similar to equation (3) and (7) where ij P is the probability of a typical response belonging to a certain format of response, i represents response, i = 1,2,3,...,n , n is the number of total responses for a certain type of response, j represents format of response, j=1 is a non-protest response, j=2 is a protest response, and j=3 is a response of noanswer. Finally, m  is a constant term and all m  s are coefficients to be estimated.

Format of hybrid type with discrete choice and open WTP revelation.
Similar to the pure discrete choice format, the type of response must, first, be classified via multinomial logit model before estimation is conducted. The final open WTP revelation is, then, estimated by modifying the bivariate probit model, where Heckman's inverse Mills ratio is generated. The final estimation of WTP with inclusion of all responses of protest, non-protest, and no-answer, i.e., the empirical specification of equation (7), is listed in the equation below (11)   (11) where all coefficients and variables have the same definition as that in (7) and Table 1 in Appendix. The mean WTP can, thus, be computed by taking the average of all estimated ij TWTP .

Results and discussions
Before analyses proceed, an overview of the full sample and subgroup of the sample for all variables is undertaken. Table 1 (see Appendix) is the summary of all variables used in different stages of estimations in the general model constructed in this study. The described subgroups are non-protest, protest, and no-answer responses. We can observe from the descriptive results that most average values of independent variables are quite similar among groups, except for a few variables. This indicates that each subgroup, i.e., non-protest, protest, and no-answer responses, has similar characteristics, thus, removing or including any subgroup of responses for analysis purpose will have similar impacts for any combination of subgroups of responses.
The percentage of respondents with occupation of doctor or in any related service sector, volunteering in environmental nongovernmental organizations (NGO) groups, and donating to environmental NGO groups for the subgroup of protest responses have relative lower mean values as compared to those of the full sample. Additionally, the protest responses are from a group of respondents that reside close to the study site. That is, they are also concerned about protection of the site, since their evaluation of the environmental function of the Wetland is not significantly lower than that of the average sample. However, they pay much more attention to the limitations on their ability to develop or utilize land after the Wetland is realized. Similar to the subsample giving protest responses, fewer among the subgroup giving no-answer responses have donated to environmental NGO groups.
The results of the estimated probability by (8) that identifies the types of responses under different elicitation formats are presented in Table 2.
Among the three subgroups, the subgroup of nonprotest responses is used as a reference group. The magnitudes of estimated results shown in Table 2 are the other two subgroups relative to the reference subgroup of non-protest responses. Once the probability of response is identified as part of each subgroup it belongs to, then, estimation of WTP for different elicitation formats will be done individually. Note: the reference group is the group of non-protest responses.
Without involving complicated and detailed WTP estimation steps for each elicitation format, the final estimated outcomes are displayed in Table 3 in Appendix for equations (3), (6), and (7). The outcomes also show the estimation results of traditional Tobit model for format of direct revelation of WTP, hybrid type format with discrete choice and open WTP revelation, and bivariate probit model for pure discrete choice format. However, the general model has the advantage of accounting for protests and no-answer response simultaneously. With accounting for both neglected and inappropriately handled subgroups for any category of elicitation format, the estimation results turn out to be statistically significant. It is easy to observe from Table 3 (see Appendix) that numbers of significant variables from the general model for any format of elicitation type are much greater than those from traditional modification and estimation.
According to the estimation results from Table 3 (see  Appendix), the corresponding annual mean WTP per household for each elicitation format can, thus, be computed. Moreover, the total WTP can also be calculated by multiplying total number of households. All the results are presented in Table 4 (see  Appendix). It clearly shows that the average WTPs per household each year are the lowest under traditional treatment for all types of elicitation formats when protestresponses are included, i.e., the results in column (C). Since such treatment normally censors the protest responses at zero, the average WTP will, then, be underestimated. In contrast, exclusion of protest responses shown as the results in column (D), has the highest average WTP per household annually.
The average WTPs per household each year are systematically higher in the traditional treatment with inclusion of non-protest responses only, and much lower for the responses with inclusion of protest responses censored at zero than the results estimated from the general model results. Although the average WTP might not be consistently higher or lower compared to results estimated from the general model, the total benefits are systematically biased downwards from traditional treatment. This set of data has 23.83% protest responses and 16.95% no-answer responses. There are 40.78% protest and no-answer responses in total. While calculating the total benefits, the total percentage of households has to reduce the same percentage as the protest and no-answer responses appear in the data. That is, there is only 59% of the total number of households accounted for when the total WTP is computed. This consistently shows that the protest responses treated by the traditional way, i.e., to exclude them or to include them in an inappropriate way, will result in underestimated total WTP.
Furthermore, the results also show that the total WTP estimated by traditional treatment for inclusion of protest responses and censored reveals that WTP or predicted WTP at zero under any format of elicitation type systematically show much more severe underestimation than those when protest responses are excluded. The degree of underestimation is ranged from a low of 26% to a high of 40%. Since traditional modification of protest responses tends to exclude them from estimation, the higher percentage of protest responses occurs the greater degree of underestimation of total estimated WTP will, then, result. The degree of underestimation is ranged from a low of 52% to a high of 67%.
The overall total WTP from the general model with inclusion of protest and no-answer responses under different types of elicitation formats is higher than those estimated by traditional treatment. The differences might arise from the average WTP estimation or the reduction of total number of households due to the exclusion of protest or noanswer responses. The results show that the general model can estimate protest responses in a relatively simple way. Most importantly, the general model can take into account no-answer responses in the estimation simultaneously. This is a big step toward resolving issues of protest and no-answer responses in the current literature.

Conclusion
The general model developed in this study is employed to deal with the protest responses and noanswer responses. This model is general in three ways: simultaneously accounting for protest and noanswer responses, its applicability to all kinds of elicitation formats in all kinds of contingent valuation applications, and its simplicity in estimation. Although there are various approaches to deal with protest responses, they are either too complicated or only suitable for specific elicitation methods. Most importantly, previous estimation methods only treat protest responses, but don't deal with no-answer responses. The general model constructed here can be used to include protest and no-answer responses at the same time. This general model mainly adopts a Heckman's inverse Mills ratio from a multinomial logit model once a group of respondents is identified as providing protest responses or no-answer responses.
To demonstrate this model, it is applied to a set of data gathered with a double-bounded choice with open-ended follow-up contingent valuation method. As such, all types of elicitation formats classified in this study will have data for demonstration. Creation of inverse Mills ratio and continuously carrying these ratios in the subsequent estimation is the distinctive step for the modification of different types of elicitation formats in our general model. The results generally indicate that these ratios are significantly different from zero. This means that accounting for these Mills ratios does have an important role in such modification when protest responses and/or no-answer responses are both taken into account. In addition to dealing with these responses, this model can be applied to samples in which the information is relatively incomplete. That is, such a model can accomplish benefit transfer between a sample with complete information and one with incomplete information.
Empirical estimations for all types of models accomplished here demonstrate the feasibility of the general model proposed in this study in dealing with protests and/or no-answer responses. Such general model can be easily used to bring into the potential excluded responses, which could cause underestimation or overestimation of mean willingness to pay or mean willingness to accept conducted by contingent valuation method. This general model is not only important, but also essential from the methodological perspective in implementing the popular evaluation method such as contingent valuation method. As the benefit, cost, or damage is a necessary component in the implementation of benefit cost analysis, evaluation with less imperfection is required. The general model proposed in this study can appropriately play such a role.    Note 1: Numbers with one, two, and three asterisks "*", "**", and "***" indicate coefficients that are significant at 10%, 5%, and 1% significance levels, respectively. Note 2: Estimation results for format of "hybrid format with discrete choice and open WTP revelation and that of "direct revelation of WTP" are the same, since the final open revelation of WTP is taken for analysis, while protest responses are included in the Tobit model.