Dealing with internal inconsistency in double-bounded dichotomous choice: an application to community-based health insurance

Contingent valuation method is commonly used in the field of health economics in an attempt to help policy makers in their policy-making decision process. The use of the double-bounded dichotomous choice format results in a substantial gain in statistical efficiency over the single-bounded dichotomous choice format. Yet, there is internal inconsistency with a downward mean shifting in the second responses. Using data from a community-based health insurance survey, this paper aims at testing whether double certainty calibration reduces internal inconsistency in a double-bounded dichotomous choice contingent valuation survey. Results suggest that double calibration significantly reduces internal inconsistency while maintaining the efficiency gain arising from the double-bounded format.     

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.     

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.     

Nonparticipation or Misspecification? The Impacts of Nonparticipation on Dichotomous Choice Contingent Valuation

Dichotomous choice (or Referendum) contingent valuation surveys have become the predominate choice for valuing goods and services otherwise not valued in a standard market (nonmarket goods and services). A number of researchers have recently recommended that dichotomous choice contingent valuation studies include a follow-up question to all no responses to determine whether the no response is a result of unwillingness to pay, or nonparticipation. If the goal of the study is to investigate the impact of covariates on either mean willingness to pay or the probability of nonparticipation, simple identification of indifferent individuals will not suffice. A simulation study shows that existing econometric models designed to account for nonparticipation are extremely sensitive to misspecification bias. Accurate identification of the probability of nonparticipation is hampered by potential misspecification of the distribution of willingness to pay.     

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.     

Protest Responses in Contingent Valuation

A significant number of respondents to contingent valuation surveys tend to either state a zero bid, or refuse to state a bid at all, for reasons associated with the process of valuation. These protest responses are routinely removed from contingent valuation samples because it is assumed that they are not indicative of respondents true values. The censoring of protest responses has led to the emergence of a definitional controversy. One view is that the definition of protest responses and the rules for censoring them are dependent on whether the practitioner conceives of the contingent valuation survey as a market or as a referendum. However, what is not acknowledged is the possibility that protest responses and their meaning may vary according to the type of good being valued, the elicitation format, and the interaction between these elements and external factors. This potential renders the development of unambiguous rules for censoring protest responses difficult. Moreover, when willingness to pay is viewed as a behavioural intention, it becomes important to determine what the responses actually mean. This approach does not assume an interpretative position a priori against which the responses should be judged, but seeks to inform an existing understanding which is inadequate.     

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 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.     

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.     

Bid Design Effects in Multiple Bounded Discrete Choice Contingent Valuation

A potential concern in multiple bounded discrete choice contingent valuation surveys – where the respondent is asked to express voting certainty, rather than a simple yes or no, on a large number of payment amounts (bids) – is whether responses are influenced by the particular position of bids in the bid-voting panel rather than solely on the respondents willingness to pay (WTP). For instance, respondents may systematically state they would pay the first few bid amounts and not pay all subsequent bids – regardless of the actual dollar values. Such systematic bid design effects would suggest that this method does not provide a valid measure of WTP. Using a split-sample survey, we compare responses to three different bid arrays that have an identical minimum bid, maximum bid, and number of bids. Using nonparametric estimation techniques, we find that estimated WTP distributions and corresponding welfare measures are not statistically different across survey samples.     

Testing Temporal Reliability and Carry-over Effect: The Role of Correlated Responses in Test-retest Reliability Studies

Test-retest studies help establish the reliability of contingent valuation (CV) responses but must confront the problem that the initial response may influence subsequent responses, and thus weaken conclusions. We develop a model that tests the influence of heterogeneous preferences and previous responses. By estimating a model of sportfishing, we show that correlation between answers to a CV question is induced by heterogeneous preferences.     

Multivariate Mixed Models for Open-Ended Contingent Valuation Data: Willingness To Pay For Conservation of Monk Seals

Although dichotomous choice (DC) contingent valuation (CV) has been recommended by the US NOAA 'blue-ribbon' panel for large-scale contingent valuation studies, useful information can still be obtained from smaller, open-ended (OE) studies, often undertaken as a precursor to a DC survey. The CV study considered here was carried out in Greece and looked at willingness-to-pay (WTP) for protecting the Mediterranean monk seal (Monachus-monachus) in the Aegean area. This is the most endangered seal in the world, and the application of the CV methodology was the first such application in Greece. The OE data consist of two responses: first, a binary response detailing whether or not respondents were in principle prepared to pay for the protection of this seal; secondly, those respondents who answered 'yes' to the first question were then asked to state their maximum WTP for such protection. A multivariate binomial – log-normal mixture model is used to develop a bid function including explanatory variables such as income, sex, age and education. Such a modelling approach provides an alternative to more commonplace tobit estimation. However, the model is extended to include further information which was collected on:(a) an increased WTP amount given in response to information that the initial WTP amount may not be enough to prevent the extinction of the seal;(b) respondents were asked to divide their final WTP amount between use, option and existence values, the latter requiring a multivariate model with four binary and four continuous responses per individual in the same model.The discussion focuses on the methodological issues raised with some comment on the substantive interpretation of results.     

The behavior of respondents in contingent valuation: Evidence on starting bids

Data from a contingent valuation survey of New Jersey beaches provides a test of starting point bias. Subsamples were delineated corresponding to levels of respondent understanding of the commodity being valued. A means- difference test showed statistically significant starting point bias for each subsample of respondents. A bid function is used to show that starting point bias is present and it increases as the level of information (understanding) decreases. Starting point bias was found even though respondents were actually using and paying for the commodity in question and the starting bids were in the neighborhood of the entry fee.     

A NONPARAMETRIC TEST FOR COMPARING VALUATION DISTRIBUTIONS IN FIRST‐PRICE AUCTIONS

This article proposes a nonparametric test for comparing valuation distributions in first‐price auctions. Our test is motivated by the fact that two valuation distributions are the same if and only if their integrated quantile functions are the same. Our method avoids estimating unobserved valuations and does not require smooth estimation of bid density. We show that our test is consistent against all fixed alternatives and has nontrivial power against root‐N local alternatives. Monte Carlo experiments show that our test performs well in finite samples. We implement our method on data from U.S. Forest Service timber auctions.     

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.     

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.     

Provision Point Mechanisms and Field Validity Tests of Contingent Valuation

Past field validity tests of contingent valuation have relied on voluntary contribution mechanisms to elicit actual willingness to pay, and may overestimate hypothetical bias because of free riding in the actual contributions. This paper argues that provision point mechanisms are a preferred alternative for field validity tests of contingent valuation because they increase the proportion of demand revealed in cases in which public goods can be provided in a step function. The results of a contingent valuation validity study of participation in a green electricity pricing program that uses a provision point mechanism are reported, and hypothetical open-ended and dichotomous choice responses are compared to actual participation. Calibration of hypothetical responses is also explored.     

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.     

Scale-perception bias in the valuation of environmental risks

The valuation of environmental risks is commonly approached with the utilization of stated preference methods such as contingent valuation. In these methods, money is utilized as the scale that reflects the individual's underlying utility function. However, this scale can vary across individuals due to different perceptions on what are the right or appropriate bounds for Willingness To Pay (WTP). In this article, we test for scale-perception bias and propose a correction method based on the utilization of anchoring vignettes that define different degrees of preference for the nonmarket good. The proposed method is applied to study the commonly found anomaly ‘probability neglect’, which is defined by the insensitivity to the probability levels in the valuation of environmental risks. The results show that probability neglect disappears when WTP responses are corrected for self-perception bias through the utilization of the anchoring vignettes approach.     

Willingness to pay for a Green Energy program: A comparison of ex-ante and ex-post hypothetical bias mitigation approaches

The most persistently troubling empirical result in the contingent valuation method literature is the tendency for hypothetical willingness to pay to overestimate real willingness to pay. Two approaches, ex-ante and ex-post, have been developed to mitigate or eliminate the overstatement of hypothetical willingness to pay. The ex-ante approach addresses hypothetical bias in the survey design stage while the ex-post approach addresses hypothetical bias with follow-up questions to the hypothetical willingness to pay question. We find that willingness to pay estimates are similar when either the ex-ante or ex-post approach are employed. Our results suggest that the approaches should be considered as complements and not substitutes. Employing both approaches to mitigate hypothetical bias we estimate that the annual benefits of the regional amenities associated with a Green Energy program in North Carolina are $186 million.