Payment certainty in discrete choice contingent valuation responses: results from a field validity test.

• Author: Vossler, Christian A.

1. Introduction

   Markets do not exist to provide the information necessary for conducting benefit-cost analyses in many public policy decision-making situations. When desired estimates of benefits or costs "are not manifest in the market" (Arrow 1999, p. vi), economists have increasingly turned to contingent valuation surveys to elicit the values that individuals would place on public goods and externalities (Mitchell and Carson 1989; Cropper and Oates 1992; Deacon et al. 1998).

   Although discrete choice, take-it-or-leave-it methods of eliciting preferences have gained favor on theoretical grounds (Arrow et al. 1993; Carson, Groves, and Machina 1999) and realism (Hanemann 1994), accumulated evidence from a number of laboratory and field contingent valuation validity studies suggests that these methods overstate actual willingness to pay (WTP) for private and public goods (e.g., Cummings, Harrison, and Rustrom 1995; Brown et al. 1996; Cummings et al. 1997; Balistreri et al. 2001; Champ and Bishop 2001). That is, respondents are more likely to say "yes" to hypothetical commitments than actual commitments, reflecting "hypothetical bias" and the need for "calibrating" contingent valuation responses (Harrison 2002).

   Two recent papers offer possible methods for calibrating hypothetical discrete-choice responses by considering payment certainty levels reported by respondents. In what we term the "follow-up certainty question" (FCQ) method, Champ et al. (1997) ask "yes" dichotomous choice respondents to indicate how certain they are, on a scale from 1 ("very uncertain") to 10 ("very certain"), that they would pay the stated dollar amount if the program were actually offered. Separate WTP functions are estimated for each certainty level. Welsh and Poe (1998) instead adopt a "multiple-bounded discrete choice" (MBDC) approach that directly incorporates certainty levels through a two-dimensional decision matrix: One dimension specifies dollar amounts that individuals would be required to pay on implementation of the policy, and the second dimension allows individuals to express their level of voting certainty through "definitely no," "probably no," "not sure," "probably yes," and "definitely yes" response options. A multiple-bo unded logit model is used to estimate separate WTP functions for each certainty level.

   In this paper, we use a field validity test of contributions to a green electricity pricing program to further explore these methods and address several validity issues. First, using actual sign-up data as a criterion, we derive "optimal" correction strategies for the two methods. Previous laboratory research on private goods suggests that "yes" hypothetical dichotomous choice responses from those who are "definitely sure" (Blumenschein et al. 1998) or at least "probably sure" (Johannesson et al. 1999) closely predict actual purchase decisions. Johannesson, Liljas, and Johansson (1998) find that respondents who are "absolutely sure" of their decision provide a conservative estimate of real purchases. These laboratory results are replicated in public goods contingent valuation field validity research using FCQ methods, suggesting that models that only use "yes" responses with certainty values on a 1-to-10 scale of "7 and higher" (Ethier et al. 2000), "8 and higher" (Champ and Bishop 2001), or "10" (Champ et al . 1997) best predict actual contributions. We are the first to provide correction strategies for the MBDC approach.

   Second, we examine if the experimental "classroom" results reported in Welsh and Poe can be replicated in the field. In that paper, the authors compare estimated logistic response distributions from dichotomous choice questions and MBDC "not sure" responses and find that they are not statistically different. This suggests that respondents who are uncertain of their values will tend to "yea-say" when asked a single dichotomous choice question, a result that has been replicated elsewhere (e.g., Ready, Navrud, and Dubourg 2001).

   Finally, in an examination of convergent validity, we compare the MBDC and FCQ methods. Specifically, we compare mean WTP, hypothetical participation rates at $6 (the actual offer price for the program), and the underlying WTP distributions estimated from various models based on the two methods, using both parametric and nonparametric estimation techniques. Conceptually, the FCQ and MBDC methods offer alternative approaches to account for respondent uncertainty in modeling contingent valuation questions. The primary difference between approaches is that the MBDC framework incorporates the certainty correction directly into the discrete choice decision framework, whereas the FCQ method can be regarded as an ex post adjustment to the dichotomous choice response. Although these questions seek the same type of information--how certain an individual is that he or she would actually pay a specified dollar amount--tests of procedural invariance have not been conducted in either the field or the laboratory.

2. Certainty Corrections within the Discrete Choice Framework

   The questioning approaches examined in this paper build on previous research indicating that contingent valuation respondents may have a distribution or range of possible WTP values rather than a single point estimate. Here we use the term "certainty" in the same sense as that in Opaluch and Segerson (1989); Dubourg, Jones-Lee, and Loomes (1994); and Ready, Whitehead, and Blomquist (1995). In this framework, when the referendum dollar threshold falls at or below the lower end of the individual's range of WTP values, then the respondent is likely to be very certain that he or she would vote in favor of the referendum. At very high amounts, the respondent might be very certain of voting against the referendum. At intermediate amounts, the respondent is less certain of how he or she actually would vote, with the level of payment certainty being inversely related to the dollar amount.

   Dichotomous Choice with FCQ

   Response certainty in the FCQ framework is incorporated as follows. Individuals first respond to a standard dichotomous choice (DC) question. For "yes" respondents, a follow-up question is asked:

   So you think that you would sign up. We would like to know how sure you are of that. On a scale from "1" to "10," where "1" is "very uncertain" and "10" is "very certain," how certain are you that you would sign up and pay the extra $6 a month if the program were actually offered?

   Respondents are asked to circle a response on the 1-to-l0 scale. As empirical evidence suggests that respondents who are uncertain about their willingness to pay tend to respond "yes" (Champ et al. 1997; Welsh and Poe 1998; Champ and Bishop 2001), a follow-up question is not asked of "no" respondents. Modeling of this approach follows well-known DC procedures in which "yes" responses are recoded for each level of certainty and separate WTP functions are estimated. For instance, one can code all responses of, say, 7 and higher as "yes" and all other responses as "no" and then employ standard DC modeling techniques.

   MBDC

   The MBDC approach contains elements of and builds on both the payment card (PC) and DC approaches widely used in contingent valuation studies. In a PC question, respondents are presented with several dollar values and asked to circle the maximum value they would be willing to pay. However, rather than circling a single value or interval as an indication of maximum WTP for the referendum, the MBDC approach provides a "polychotomous choice" response option including, say, "definitely no," "probably no," "not sure," "probably yes," and "definitely yes." The respondent then chooses a response option for each of the dollar amounts. In this manner, the context of the good-to-cost trade-off is expanded beyond traditional DC or PC questions by including additional dollar amounts and the likelihood of voting yes, respectively. In some sense, the MBDC model might be thought of as a general framework from which the DC and the PC techniques can be derived as special cases.

   Analysis of WTP data collected using the MBDC technique is conducted using a multiple-bounded generalization of single- and double-bounded DC models in which the sequence of proposed dollar values divides the real number line into intervals (Harpman and Welsh 1999). An individual's response pattern reveals the interval that contains his or her WTP at a given level of certainty. Defining [X.sub.iL] as the maximum amount that the ith individual would vote for and [X.sub.iU] to be the lowest amount that the ith individual would not vote for, [WTP.sub.i] lies somewhere in the switching interval [[X.sub.iL] [X.sub.iU]]. Let F([X.sub.i]; [beta]) denote a statistical distribution function for [WTP.sub.i] with parameter vector [beta]. The probability that an individual would vote against a specific dollar amount, [X.sub.i], is simply F([X.sub.i]; 3). Therefore, the probability that a respondent would vote "yes" at a given dollar amount, [X.sub.i] is 1 - F([X.sub.i]; [beta]). The probability that [WTP.sub.i] falls bet ween the two price thresholds, [X.sub.iL] and [X.sub.iU] is F([X.sub.iU]; [beta]) - F([X.sub.iL]; [beta]), resulting in the following log-likelihood function:

   lnL = [summation over (n/i=1) ln[F([X.sub.iU]; [beta]) - F([X.sub.iL]; [beta])].

   When the respondent says "yes" to every amount, [X.sub.iU] 4. Likewise, when the respondent says "no" to every amount, [X.sub.iL] = -4. It should be apparent that the previous equation represents the log-likelihood function for discrete choice models in general, including the DC model (Welsh and Poe 1998). This likelihood function also parallels that used for analysis of interval data from payment cards (Cameron and Huppert 1989).

   Within this framework, WTP functions can he estimated based on any of the voting certainty levels. For example, a "definitely yes" model corresponds to modeling the lower end of the switching...