Identifying inconsistent responses in dichotomous choice contingent valuation with follow-up questions

We develop a new but simple non-parametric method to diagnose inconsistency in double-bounded contingent valuation questions in the presence of both perfect and imperfect correlation between initial and follow-up response distributions. The proposed method can identify inconsistency in iterative responses at each bid interval. We apply this method to data from five well-known double-bounded contingent valuation surveys. The predictions of our model match closely with parametric outcomes. Further, we find that the inconsistency patterns generally vary for different data sets and different bid intervals within data sets. Therefore no single behavioral model can explain all latent inconsistency patterns either within or across data sets. In addition, we examine the impact of inconsistency in responses on bias and efficiency of the double-bounded format in the absence of correction for inconsistency. We conclude that the commonly cited benefits of the double-bounded format hold only in the special case of nearly perfect consistency between initial and follow-up response distributions. Our method provides a simple tool researchers can use to determine the similarity in response distributions between the initial and follow-up responses and whether incorporating collected follow-up responses are likely to actually increase efficiency without introducing bias.     

Does Question Format Matter? Valuing an Endangered Species

A three-way treatment design is used to compare contingent valuation response formats. Respondents are asked to value an endangered species (the red-cockaded woodpecker) and the restoration of its habitat following a natural disaster. For three question formats (open-ended, payment card, and double-bounded dichotomous choice), differences in survey response rates, item non-response rates, and protest bids are examined. Bootstrap techniques are used to compare means across formats and to explore differences in willingness to pay (WTP) distribution functions. Convergent validity is found in a comparison of mean WTP values, although some differences are apparent in the cumulative distribution functions. Differences across formats are also identified in item non-response rates and proportion of protest bids. Overall, the payment card format exhibits desirable properties relative to the other two formats.     

A multilevel modelling approach to triple-bounded dichotomous choice contingent valuation

The use of dichotomous choice (DC) questions in the elicitation of willingness to pay (WTP) in contingent valuation studies is common practice at the present time. Recent research has shown that double-bounded DC questions provide statistically superior results to single-bounded questions, given an appropriate sampling design. This paper uses a relatively new multilevel modelling technique to analyze a triple-bounded DC design, which in addition includes an initial non-monetary question on whether an individual accepts, in principle, a WTP some unspecified amount. The theoretical basis of the multilevel model used is described, and some of the possibilities of this potentially powerful and versatile technique are discussed. The practical operation of the multilevel model is demonstrated using data from a contingent valuation study conducted in the Norfolk Broads, England, an internationally important wetland resource.     

A Bayesian Approach to Double Bounded Contingent Valuation

In this paper we propose a Bayesian approach to model double bounded contingent valuation data. The double bounded elicitation method is interpreted as a two tier iterated process in which the subject is allowed to have a second thought about his/her valuation for the environmental good. Prior information is modelled from the answers to the first dichotomous choice question. The model is Quasi-Bayesian (Q-B) in that the prior distribution refers to mean willingness to pay while the likelihood function refers to the proportions of a multinomial distribution. This model is applied to empirical data from a contingent valuation survey involving the valuation expressed by European tourists for access to natural areas in the Canary Islands. Results show that point estimate of consumer surplus computed with the Q-B model does not differ substantially from single bounded model estimation. In addition, double bounded seems to be quite robust to the choice of the prior model of willingness to pay responses. Comparison with open ended suggests that the Q-B model might be useful to control for strategic response and starting point biases.     

A Semi-parametric Estimator of Willingness-to-pay Applied to Dichotomous Choice Contingent Valuation Data

The use of dichotomous choice questions (Are you willing to pay $x?) has been advocated as superior to open ended questions (What would you be willing to pay?) in contingent valuation studies of non‐market goods. A supplementary dichotomous choice question, raising or lowering the bid price depending on the initial response, gives increased precision. However, a problem with these methods is that identifying the mean willingness to pay (WTP) is more complex, and often conditional on making a distributional assumption. This paper will present a semi‐parametric method for estimating WTP without invoking any such assumptions, using the interval inherent in the double bounded format, and based on estimating the underlying hazard function for the distribution of WTP. An advantage of the approach over other non‐parametric methods is that it allows one to include respondent characteristics as determinants of the individual decisions, and does so within a computationally straightforward framework.     

Bound and path effects in double and triple bounded dichotomous choice contingent valuation

Dichotomous choice contingent valuation questions are relatively inefficient in that large sample sizes are required for a given level of estimation precision. An increasingly common approach to this problem is to supplement the initial question with subsequent dichotomous choice questions in a multiple-bound design. However, a number of commentators have suggested that such designs may generate responses which are internally inconsistent in that the distribution of underlying preferences implied by answers to the initial question may not be the same as that implied by the entire sequence of replies. We consider a variety of potential causes of such inconsistencies and use data from a contingent valuation study with two follow-ups and post survey debriefing focus groups to test both the effects caused by moving from one bound to another and those caused when respondents follow either the bid-increasing path generated by a positive response at a given bid amount, or the bid-decreasing path generated by negative responses. Results indicate that both bound and path effects are significant and generate a pattern corresponding to certain of the causes of inconsistency identified in the paper. Conclusions for the future application of such designs are presented.     

Application of Sample Selection Model to Double-Bounded Dichotomous Choice Contingent Valuation Studies

Modeling households' behavior with the data from a contingentvaluation (CV) survey is often complicated by samplenon-response, which can cause non-response bias and sampleselection bias, leading to inconsistent parameter estimates and adistorted mean willingness-to-pay estimate. This paper reportsthe results of empirical tests for both biases using householdsurvey data in which the double-bounded dichotomous choice CVquestion involved the benefit of a tap water quality improvementpolicy in Korea. No non-response bias, but sample selection bias,is detected in the sample. To correct for sample selection bias,a sample selection model is employed. The authors also discusshow failure to correct for bias may distort aggregate benefitestimates.     

Starting point bias and respondent uncertainty in dichotomous choice contingent valuation surveys

In this article, we develop a dichotomous choice model with follow-up questions that describes the willingness to pay being uncertain in an interval. The initial response is subject to starting point bias. Our model provides an alternative interpretation of the starting point bias in the dichotomous choice valuation surveys. Using the Exxon Valdez survey, we show that, when uncertain, individuals tend to answer “yes”.     

Heterogeneous anchoring and the shift effect in iterative valuation questions

In this article, we consider starting point bias as a heterogeneous phenomenon, that is, respondents in contingent valuation surveys do not anchor in the same way. We study the consequences of a mistaken assumption of homogeneous anchoring for the analysis of the shift effect in multiple-bounded dichotomous choice format, when respondents really have heterogeneous anchoring. We show that the shift effect, generally interpreted as incentive incompatibility or “yea”-saying, can be the spurious outcome of disregarded heterogeneous anchoring.     

Joint Estimation of Multiple CVM Scenarios under a Double Bounded Questioning Format

Contingent valuation surveys frequently ask the same respondent for willingness to pay (WTP) for either different programs or different levels of provision of a single program. When multiple scenarios are considered by the respondent, the errors in the estimates of WTP are likely to be correlated across scenarios. Failing to account for correlation may lead to erroneous inferences concerning differences in WTP. This paper presents a technique that can be used to jointly estimate WTP for multiple scenarios proposed within a survey when the double-bounded questioning format is used. Monte Carlo simulations are employed to show that estimates derived from the joint model provide lower parameter variances as well as tighter confidence intervals surrounding WTP. The model is used to estimate WTP values for data collected in telephone interviews of California residents concerning WTP for fire reduction programs in Oregon and California. Variance properties of these estimates are shown to be similar to those estimated using simulated data.     

Induced-Value Tests of Contingent Valuation Elicitation Mechanisms

Using an induced-value experimental design that varies whether values for a “good” are certain or uncertain and whether payment is real or hypothetical, this study investigates issues of demand revelation, hypothetical bias, and value uncertainty for four elicitation mechanisms used in contingent valuation surveys: dichotomous choice, dichotomous choice with follow-up certainty question, payment card, and multiple-bounded discrete choice. For all elicitation mechanisms, we find no evidence of hypothetical bias: voting decisions do not vary systematically when payment is hypothetical versus when it is real. Under all design conditions we find the fewest deviations between stated and induced values and the strongest evidence of demand revelation with dichotomous choice. Stated uncertainty in dichotomous choice follow-up and multiple-bounded discrete choice questions does correlate with uncertain induced values, but the signal is noisy. We discuss the implications of our findings for the design of contingent valuation surveys.     

Implications of Bid Design and Willingness-To-Pay Distribution for Starting Point Bias in Double-Bounded Dichotomous Choice Contingent Valuation Surveys

We examine starting point bias in double-bounded dichotomous choice contingent valuation surveys. We investigate (1) the seriousness of the biases for the location and scale parameters of the willingness-to-pay (WTP) in the presence of starting point bias; (2) whether or not these biases depend on the distribution of WTP and on the bid design; and (3) how well a commonly used diagnostic for starting point bias—a test of the null that bid set dummies entered in the right-hand side of the WTP model are jointly equal to zero—performs under various circumstances. Monte Carlo simulations suggest that the effect of ignoring starting point bias depends on the bid design and on the true distribution of WTP. A well-balanced, symmetric bid design may result in very modest biases even when the anchoring mechanism is very strong. The power of bid set dummies in detecting starting point bias is low. They tend to account for misspecifications in the distribution assumed by the researcher for the latent WTP, rather than capturing the presence of starting point bias.     

Some notes on trichotomous choice discrete valuation

For some respondents, the bid offered by the dichotomous choice format used in the discrete choice technique can in fact be the true optimum. In this case the correct answer is neither yes or no, but indifferent. We shall show results from a trichotomous choice format and analyse whether it produces welfare measures with narrower confidence intervals than the dichotomous technique. Another well known problem in contingent valuation (CV) studies is that the volume of the good to be purchased from hypothetical markets is not, in many cases, defined in precise terms. We show how the trichotomous choice technique can be used to test for possible vagueness in the volume of the project to be valued.     

Are There Income Effects on Global Willingness to Pay for Biodiversity Conservation?

This paper is concerned with the empirical relationship between biodiversity conservation values and income. We use random effects panel models to examine the effects of income, and then GDP per capita, on willingness to pay for habitat and biodiversity conservation. In a meta-analysis, 145 Willingness To Pay estimates for biodiversity conservation where existence value plays a major role were collected from 46 contingent valuation studies across six continents. Other effects included in the meta-analysis were the study year; habitat type; continent; scope as presented to respondents; whether WTP bids were for preventing a deterioration or gaining an improvement in conservation, whether a specific species or specific habitat was protected; whether the questionnaire used a dichotomous choice or an open-ended format; distribution format; and the choice of payment vehicle. GDP per capita seemed to perform as well as an explanatory variable as respondent’s mean stated income, indicating that it is wealth in society as a whole which determines variations in WTP. Even if large variation, our main conclusion is, that the demand for biodiversity conservation rises with a nation’s wealth, but the income elasticity of willingness to pay is less than one.     

Evaluating the Validity of the Dichotomous Choice Question Format in Contingent Valuation

Hypothetical and actual cash willingness to pay (WTP) for an art print were elicited with dichotomous choice and open-ended question formats. Comparing hypothetical and actual dichotomous choice responses using both a likelihood ratio test and the method of convolutions suggests we reject equality at the 0.05 but not the 0.01 level. Hypothetical WTP was roughly two times actual WTP with the dichotomous choice format. There were no significant differences between the open-ended and dichotomous choice question formats when both were used to estimate hypothetical WTP or both used to estimate actual WTP.     

Effects of information about invasive species on risk perception and seafood demand by gender and race

In this paper we consider the effects of negative and positive risk information on perceived seafood risks and seafood consumption by gender and race. The data is from a Mid-Atlantic survey of coastal seafood consumers. We elicit risk perceptions in three risk scenarios with a dichotomous choice with a follow-up question format. We elicit continuous revealed and stated preference seafood consumption in nine risk and price scenarios. Analysis in four gender and race categories indicates that demographic groups respond to the positive and negative information in different ways. Communication of risk information as risk mitigation policy is a challenge.     

A Learning Design for Reducing Hypothetical Bias in the Contingent Valuation Method

Over the last few years a great deal of research has focussed on hypothetical bias in value estimates obtained with the contingent valuation (CV) method and on means for ameliorating if not eliminating such bias. To date, efforts to eliminate hypothetical bias have relied on calibration techniques or on word-smithing of one kind or another to induce subjects to provide responses to hypothetical questions that mimic responses made by subjects facing actual payments in the valuation experiment. This paper introduces a different approach for eliminating hypothetical bias. A design for a CV survey format is presented which provides subjects with the opportunity to learn how the CV institution works. Sequential referenda are conducted where respondents gain experience in CV settings by participating in both hypothetical and real referenda. The logic of this Learning Design is a straightforward application of the trials process used in experimental economics. We demonstrate that the Learning Design is effective in eliminating hypothetical bias in surveys concerning donations to two different public goods.     

Joint estimation of contingent valuation survey responses

Hanemann's utility difference model for the dichotomous choice contingent valuation method is modified to account for interrelationships between responses to a set of contingent valuation questions. A nonlinear seemingly unrelated regression model is presented to jointly estimate the probit models and to derive WTP from the CV responses. The model is used to test and impose restrictions derived from economic theory on the utility difference model. Mean WTP estimates for three different types of changes in the quality of California deer hunting were uniformly lower for the joint response probit model compared to a set of independent probit models.     

Repeated Dichotomous Choice Formats for Elicitation of Willingness to Pay: Simultaneous Estimation and Anchoring Effect

Repeated dichotomous choice contingent valuation data are generated from responses to a succession of binary questions regarding alternative prices for an environmental good. In this paper we propose a simultaneous equation model that allows for endogeneity and error correlation across the responses at each stage of the bidding process. The model allows us to study the evolution of anchoring effects after the second dichotomous choice question. Estimation involves the Bayesian techniques of Gibbs sampling and data augmentation, and the application focuses on the preservation value of a natural area. The results for a data set involving up to four successive dichotomous choice questions show that restricted multiple-bounded models are rejected by the data with the general model. In addition, willingness to pay tends to stabilize after the second stage in the elicitation process for the general unrestricted model. When taking anchoring effects into consideration, it is revealed that individuals’ responses in the latter stages are influenced by the sequence of bid prices offered in earlier questions. Nevertheless, they do not have a significant effect on welfare estimates.      

Modelling unobserved heterogeneity in contingent valuation of health risks

Human preferences for alternative levels of health risks can be heterogeneous. In this paper a flexible distribution approach to model health values elicited with the dichotomous choice contingent valuation method is considered. Rigid parametric structures cannot model sample heterogeneity while imposing strong assumptions on the error distribution. A mixture of normal distributions is considered which can approximate arbitrary well any empirical distributions as the number of mixtures increases. The model is applied to data on willingness to pay for reducing the individual risk of an episode of respiratory illness. The mixture distribution model is compared with the rigid probit model using a Bayes factor test. The results show that the mixture modelling approach improves performance while allowing for the consideration of alternative groups of individuals with different preferences for health risks.