Elicitation Effects in Contingent Valuation: Comparisons to a Multiple Bounded Discrete Choice Approach

JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT ARTICLE NO.

36, 170᎐185 Ž1998.

EE981043

Elicitation Effects in Contingent Valuation: Comparisons to a Multiple Bounded Discrete Choice Approach1 Michael P. Welsh Senior Associate, Hagler Bailly Consulting Incorporated r Stratus Consulting Incorporated, 455 Science Dri¨ e, Madison, Wisconsin 53711

and Gregory L. Poe* Assistant Professor, Department of Agricultural, Resource, and Managerial Economics, Cornell Uni¨ ersity, Ithaca, New York 14853 Received June 12, 1996; revised June 18, 1998 This paper develops a multiple bounded discrete choice elicitation technique that allows respondents to express their level of voting certainty for a wide range of referendum thresholds. The paper concludes with the results of an empirical study comparing values obtained from a multiple bounded model with values derived from three standard contingent valuation elicitation formats: dichotomous choice, payment card, and open-ended. The multiple bounded discrete choice format covers the range of values associated with the other three predominantly used elicitation methods. Moreover, alternative parameterizations of the multiple bounded discrete choice model correspond to these standard elicitation techniques. 䊚 1998 Academic Press

1. INTRODUCTION Contingent valuation practitioners, experimental economists, and psychologists have long recognized that the use of different contingent valuation elicitation formats can result in divergent value estimates w9, 12, 32x. Comparisons of field and laboratory elicitation studies, for example, indicate that there are systematic and significant differences between values elicited using continuous Že.g., open-ended and payment card. and discrete choice contingent valuation formats w4, 29x. While there are some exceptions Že.g., w3x., values collected using dichotomous choice ŽDC. formats typically exceed values collected using open-ended ŽOE. formats. Comparisons of discrete choice values and payment card values show a similar 1 Senior authorship is shared. The authors are indebted to Dick Aplin, Cindy van Es, Ed McLaughlin, Bill Schulze and their classes for participating in this experiment. Rich Bishop, Rich Ready, Bill Schulze, and W-133 participants offered helpful insights on this project. We also thank two anonymous reviewers for their insights. However, the authors remain responsible for any remaining errors. Funding was provided by Cornell University Agricultural Experiment Station under Regional Project W-133 Benefits and Costs Transfers in Natural Resources Planning. Permission to use and modify pilot survey instruments developed by Glen Canyon Environmental Studies ŽU.S. Bureau of Reclamation. is greatly appreciated. *Correspondence should be addressed to either author at e-mail [email protected] or [email protected]

170 0095-0696r98 $25.00 Copyright 䊚 1998 by Academic Press All rights of reproduction in any form reserved.

MULTIPLE BOUNDED DISCRETE CHOICE

171

relationship, with discrete choice values exceeding those obtained from payment cards ŽPC..2 Evidence of elicitation effects has played a role in the continuing controversy over the use of contingent valuation. Some experts suggest that the discrete choice format is the preferred format w2x. Others have suggested that failure to demonstrate consistency across value elicitation formats forms a basis for rejecting the validity of contingent valuation altogether Že.g., w22, 10, 28x.. We maintain that it is premature to dictate a preferred valuation format or to conclude that these observed differences in values indicate that contingent valuation is unreliable. Both issues merit further investigation in controlled experiments and actual valuation studies in order to better quantify or calibrate differences between elicitation formats and to begin to understand factors that contribute to these persistent differences. In this paper we begin to address some of these issues by exploring the hypothesis that contingent valuation respondents invoke different decision heuristics when asked to assign a value to a good, as in the OE or PC techniques, or to make a direct choice, as in the DC elicitation technique. To accomplish this goal, a multiple bounded discrete choice ŽMBDC. model is introduced, which allows respondents to vote on a wide range of referendum thresholds. At each referendum threshold the respondent is asked, using a scale from ‘‘Definitely No’’ to ‘‘Definitely Yes’’, to indicate how hershe would vote if passage of the referendum cost them that amount. Valuation functions and willingness to pay ŽWTP. estimates associated with different certainty levels from the MBDC model are then compared to PC, OE, and DC response functions using a contingent valuation study of Glen Canyon Dam operations. The paper is organized as follows. The next section introduces the MBDC approach. The valuation experiment and data is discussed in Section 3 and empirical comparisons across elicitation formats are presented in Section 4. The final section discusses the implications of this research. 2. MULTIPLE BOUNDED DISCRETE CHOICE FORMAT The MBDC format is adapted from the ‘‘return potential’’ format w18, 30x used by sociologists to explore the strength of social norms Že.g., crowding. and satisfaction levels across varying conditions Že.g., boating parties encountered.. The typical return potential question format is a two-dimensional matrix, in which one dimension delineates differing levels of the commodity and the other elicits intensity of preference. For example, in a study of the effects of stream flow on Grand Canyon river rafting recreational benefits, Shelby et al. w31x asked respondents to rate 14 different stream flow levels ranging from 1 Žvery satisfactory . to 5 Žvery unsatisfactory.. Welsh and Bishop w33x demonstrated that this Žordinal. return potential format could be adapted to provide Žcardinal. contingent valuation estimates of WTP by describing a referendum over whether or not to pursue public provision of a 2

Notably, in a number of studies of recreation and other public goods the ratio of DC values to OE values falls in the range from 1.1 to 5 Žalthough McFadden w22x reports DC to OE ratios greatly exceeding 10 for wilderness protection.. Two comparisons of DC with PC values provide DCrPC ratios of a similar magnitude: Haefele et al. w13x and Ready et al. w27x report DCrPC ratios of 3.3 and 3.6᎐4.4, respectively.

172

WELSH AND POE

nonmarket good. The first dimension over which respondents are asked to make choices is the dollar amount that they would be required to pay if the referendum passed. The second dimension allows individuals to express their level of voting certainty for the referendum at each dollar value. An example of this approach is provided in Fig. 1. This proposed MBDC approach contains elements of, and builds upon, both the PC and DC approaches widely used in contingent valuation studies. Like the PC format, respondents are presented with an ordered sequence of dollar thresholds. Yet, rather than circling a single value or interval, the respondent is given a ‘‘polychotomous choice’’ response option, as in Ready et al. w26x, including, say, ‘‘Definitely No’’, ‘‘Probably No’’, ‘‘Not Sure’’, ‘‘Probably Yes’’, and ‘‘Definitely Yes’’. This response format allows the respondent to express a level of voting certainty associated with each dollar threshold. In this manner, the context of the good-to-cost tradeoff is expanded beyond traditional DC or PC questions by

FIG. 1. Multiple boundedrreturn potential question format.

173

MULTIPLE BOUNDED DISCRETE CHOICE

including additional dollar thresholds and likelihood of voting yes. 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. This questioning approach builds upon suggestions by previous researchers that rather than having a single point estimate of the value for the environmental good, contingent valuation respondents may instead have a distribution or range of possible WTP values w16, 23, 11, 6x. In this vein, the MBDC allows contingent valuation respondents to express their certainty that they would vote in favor of a referendum to provide the contingent valuation good for a range of dollar thresholds. Here we use the term ‘‘certainty’’ in the same sense as that in Opaluch and Segerson w23x, Ready et al. w26x, Duborg et al. w11x, and Champ et al. w8x. When the referendum dollar threshold falls at or below the lower end of the individual’s range of WTP values, then the respondent may be very certain that he or she would vote in favor of the referendum. Likewise, at very high amounts the respondent might be very certain of voting against the referendum. Analysis of WTP data collected using the MBDC technique is conducted using a multiple bounded generalization of double bounded models w15, 33x, analogous to the maximum likelihood interval modeling approach used for PC data w5x. The modeling of this approach is most easily understood by first considering the case where the individual has the option of simply responding ‘‘Yes’’ or ‘‘No’’ to a series of dollar thresholds rather than expressing a level of voting certainty. Defining X i L as the maximum dollar threshold that the ith individual would vote for, and X iU to be the lowest dollar threshold that the ith individual would not vote for, WTPi lies somewhere in the switching interval w X i L , X iU x. Let F Ž X i ; ␤ . denote a statistical distribution function for WTPi with parameter vector ␤ . The probability that an individual would vote against a specific dollar amount, X, is simply F Ž X i ; ␤ .. Therefore, the probability that a respondent will vote ‘‘Yes’’ at a given dollar amount, X, is 1 y F Ž X i ; ␤ .. The probability WTPi falls between any two price thresholds is F Ž X iU ; ␤ . y F Ž X i L ; ␤ ., resulting in the corresponding log-likelihood function n

ln Ž L . s

Ý ln F Ž X iU ; ␤ . y F Ž X i L ; ␤ .

.

Ž 1.

is1

When the respondent says ‘‘Yes’’ to every amount, X iU s ⬁. Likewise, when the respondent says ‘‘No’’ to every amount, X i L s y⬁. It should be apparent that Eq. Ž1. represents the log-likelihood function for discrete choice models in general. The log-likelihood function for both the DC and the double bounded model can be expressed in this form w15, 33x. This likelihood function also parallels that used for analysis of interval data from payment cards w5x. This bounded likelihood model can be applied to each of the positive voting certainty levels associated with the MBDC model. For example, a ‘‘Definitely Yes’’ model corresponds to modeling the lower end of the switching interval at the highest amount the individual chose the ‘‘Definitely Yes’’ response category and the higher end of the switching interval at the next dollar threshold. Similarly, a ‘‘Probably Yes’’ model sets the lower end of the switching interval at the highest amount the individual chose the ‘‘Probably Yes’’ response category. Finally, a ‘‘Not Sure’’ MBDC model sets the lower end of the switching interval at the

174

WELSH AND POE

highest amount at which the individual chose the ‘‘Not Sure’’ response category.3 To illustrate the differences using the referendum amounts shown in Fig. 1, suppose a respondent chose ‘‘Definitely Yes’’ at $10 and lower, ‘‘Probably Yes’’ at $20 and $30, ‘‘Not Sure’’ at $40, ‘‘Probably No’’ at $50 and $75, and ‘‘Definitely No’’ at $100 and above. The switching interval for ‘‘Definitely Yes’’ model would be w$10, $20x. For the ‘‘Probably Yes’’ model the switching interval would be w$30, $40x, and for the ‘‘Not Sure’’ model the switching interval would be w$40, $50x. Statistical models across individuals can be estimated by assuming that individuals have different underlying preferences and response patterns. 3. VALUATION EXPERIMENT In this section we compare the MBDC approach with PC, DC, and OE elicitation techniques using experimental survey data collected at Cornell University in 1994 and 1995. To accomplish this goal, a split sample experiment was designed in which each sample received a DC, PC, OE, or MBDC question. In 1994, efforts were directed toward comparing the MBDC method with its most closely related question formats, DC and PC. A total of 557 observations were split roughly evenly between PC, DC, or MBDC questionnaires. In 1995, the research instead focused on comparing OE and MBDC response patterns, with elicitation questionnaires split about evenly between the two methods across 188 participants. Because of possible sample effects across the years, no effort is made to compare the 1994 and 1995 data. Consequently, the 1994 and 1995 samples are treated as separate noncomparable samples throughout this analysis. Rather than design a completely new survey instrument, a pilot study of WTP for reduced fluctuations in Glen Canyon Dam releases, developed by Glen Canyon Environmental Studies, was used. This survey instrument had been extensively pretested, peer reviewed, and approved for a federally funded contingent valuation survey w34, 35, 36x. The pilot survey instrument used in Glen Canyon Environmental Studies was modified in length and content to allow for classroom distribution. The resulting nine-page questionnaire and associated six-page information sheet were distributed to five Cornell undergraduate classes in the Department of Agricultural, Resource, and Managerial Economics. In each class, the objectives of the experiment were discussed, and briefly related to the subject matter in the course. The students were informed that each student returning a fully completed questionnaire could participate in a lottery for $100 in prizes in each class. Two 1994 classes and one 1995 class allocated 30 min for completing the questionnaire in the classroom, with an associated response rate of 96 percent Ž692r724.. The 3

This approach is perhaps the simplest way of dealing with uncertainty expressed in the responses to the multiple bounded question. As an alternative, one could imagine constructing a multiple bounded polychotomous model in which the researcher estimates the probability of each response category at each dollar amount. A second approach would be to explicitly incorporate the information revealed about uncertainty into the estimation procedure such as was done in Li and Mattson w21x. In this second approach the researcher could possibly exploit the fact that the respondent reveals lower levels of uncertainty for some of the thresholds than for others. The approach taken in this paper was selected because it allows relatively simple and direct comparisons between elicitation techniques. Conceptually the ‘‘Probably No’’ and the ‘‘Definitely No’’ models could also be evaluated. However, the likely upward bias associated with hypothetical questions and the difficulty of attaching a ‘‘Yes’’ interpretation to negative responses warrants exclusion from our analyses.

MULTIPLE BOUNDED DISCRETE CHOICE

175

students in the other two 1994 classes were instructed to return their completed questionnaires at the following class meeting, providing a lower response rate of 57 percent Ž128r226.. Before completing the questionnaire, the student subjects were instructed to first read the six-page information sheet consisting of a map and information about the dam, the study area, and the relationship between the Glen Canyon Dam and the study area. Particular emphasis was given to describing the existing natural resources, archeological sites, and fish populations, and the present and future status of these resources as a function of in-stream flows as controlled by the operation of the hydroelectric facility at the Glen Canyon Dam.4 An existence value component was emphasized in the information sheet by noting that only a small percentage of the visitors to the Grand Canyon National Park actually see or use the resources in the study area, and that ‘‘the only people who see the resources in the study area are American Indians using resources in the study area, people who raft andror backpack, and people who fish there.’’ A comprehensive truerfalse quiz at the beginning of the questionnaire encouraged reading and assimilation of the information provided. Following this quiz, a hydroelectric management ‘‘proposal’’ ŽFig. 2. that would eliminate daily fluctuations in the river level and mimic, to the extent possible, natural seasonal fluctuations was described. In each version of the survey, respondents were first asked if they would vote in favor of the proposal if passage of the proposal did not personally cost them anything. Participants indicating they would vote for the proposal at zero cost were then asked a contingent valuation question. The MBDC ŽFig. 1. and PC questions consisted of identical series of 13 dollar thresholds ranging from 10¢ to $200 per annum. DC bids were individually inscribed in the appropriate space on the DC questionnaire, with each DC participant receiving one of nine values between $1 and $200 Ž$1, $5, $10, $20, $30, $50, $100, $150, $200.. To retain parallel wording with the other formats, the OE format was framed as a voting situation rather than simply asking for ‘‘maximum willingness to pay’’. For reference, the text of the alternative question formats is provided in the Appendix. 4. RESULTS To facilitate statistical testing, the DC, PC, and OE response models were treated as special cases of the bounded-likelihood function provided in Eq. Ž1.. The likelihood function for the MBDC model is completely defined by the probabilities associated with the endpoints of the interval revealed to contain WTP. Thus, the PC data, the OE data, and the DC data can be modeled using the MBDC approach by identifying the end points of an interval containing WTP and estimating the value of FŽ.., the cumulative distribution function ŽCDF. for WTP, at each of these endpoints. For each respondent, the PC data identifies the range bounding maximum WTP Žsee w5x.. To illustrate, if a respondent selected the PC response category of $20, 4 This information set was not modified from that used in the Glen Canyon Environmental Studies materials. These materials were developed in conjunction with a panel of physical and biological researchers familiar with the effects of dam operation on the river-related resources in the Grand Canyon. Materials were also extensively evaluated in focus groups and in a large scale pilot test.

176

WELSH AND POE

FIG. 2. Base scenario, all versions.

WTP was inferred to fall on the interval between $20 and $30 Žthe next higher value on the payment card.. The OE responses were converted to a bounded interval data set by creating a switching interval with a lower bound Ž X i L . of OE i y 0.01 and an upper bound Ž X iU . of OE i q 0.01 for each response. This was done to facilitate statistical comparisons by allowing the OE responses to be modeled with the same bounding framework used to analyze data collected from other elicitation techniques. The DC data is treated in an analogous fashion. If a respondent answers ‘‘Yes’’ to a DC threshold, WTP is revealed to exceed the DC threshold. Since the upper end of the interval containing WTP is not observed, the probability associated with ‘‘Yes’’ responses is simply 1 y F Ž X i L ; ␤ . where X i L is set equal to the DC threshold. For ‘‘No’’ responses, WTP is revealed to be less than the DC threshold. In such a case, the lower end of the interval containing WTP is not observed so the probability associated with this observation is simply F Ž X iU ; ␤ . where X iU is set equal to the DC threshold Žsee w14x..

177

MULTIPLE BOUNDED DISCRETE CHOICE

The hypothesis of equality between estimated maximum likelihood response functions can be evaluated using the likelihood ratio ŽLR. test: LR s 2) Ž ll 1 q ll 2 . y ll pool ; ␹ 2 Ž r . ,

Ž 2.

where ll 1 and ll 2 are the log-likelihood values associated with the individual models to be compared, ll pool is the log-likelihood value associated with the pooled model imposing equality of coefficients Ž ␤ ., and r is the number of restrictions. Voting patterns on the ‘‘no cost’’ proposal in Question 2 ŽFig. 2. were similar across elicitation formats, as would be expected by the fact that this question preceded the contingent valuation questions. The percent voting ‘‘Yes’’ to the ‘‘no cost’’ proposal ranged from 92.4% to 95.5%.5 Conditional response patterns for the ‘‘Yes’’ respondents to the ‘‘no cost’’ proposal are provided in Table I. The first column contains the referendum dollar thresholds. The next ten columns provide the distribution of MBDC responses for each threshold by year. PC, DC, and OE response patterns are indicated in the last three columns. DC and PC responses exhibit patterns observed in previous research. The proportion of DC ‘‘Yes’’ responses generally declines as threshold values increase.

5

The percent not supporting the ‘‘no cost’’ project does not vary significantly across survey versions. These individuals are dropped from the subsequent analysis. This allows us to focus our methodological comparisons on data collected from individuals with positive values. In a policy study, these individuals would have to be formally included in the analysis. This could be accomplished in one of several ways, for example by estimating a model that allows for a ‘‘spike’’ of values at $0, by including $0 as the lowest bound in the multiple bounded analysis, or by assigning these individuals a value of zero and calculating a population weighted average WTP.

TABLE I Actual Response Distributions MBDC Ž%. a Def. No

10¢ 50¢ $1 $5 $10 $20 $30 $40 $50 $75 $100 $150 $200 a

Prob. No.

Not Sure

Prob. Yes

Def. Yes

PC Ž%.

DC Ž% yes.

OE Ž%.

1994

1995

1994

1995

1994

1995

1994

1995

1994

1995

1994

1995

1994

0.0 0.5 0.5 3.6 6.8 12.5 18.2 25.0 29.7 35.9 46.4 53.6 60.7

0.0 0.0 0.0 0.0 4.2 6.3 13.5 16.7 18.8 30.2 41.7 50.0 56.3

0.5 0.5 0.5 3.6 5.7 10.9 13.5 12.0 16.1 18.8 20.8 22.4 17.8

0.0 0.0 0.0 6.3 6.3 11.5 10.4 14.6 22.9 21.9 26.0 29.2 24.2

0.5 1.6 4.7 11.5 15.6 18.2 20.8 24.5 27.1 28.6 23.4 18.2 16.8

0.0 0.0 3.1 5.2 11.5 12.5 25.0 26.0 26.0 25.0 19.8 12.5 11.5

6.8 9.4 13.6 20.3 29.2 28.1 29.7 27.1 19.8 13.0 6.8 4.2 3.7

1.0 8.3 9.4 21.9 32.3 41.7 29.2 26.0 19.8 17.7 8.3 6.3 6.3

92.2 88.0 80.6 60.9 42.7 29.7 17.7 11.5 7.3 3.6 2.1 1.6 1.0

99.0 91.7 87.5 66.7 45.8 28.1 21.9 16.7 12.5 5.2 4.2 2.1 2.1

2.7 3.2 9.6 12.8 20.2 10.1 4.8 7.4 14.9 1.6 8.5 1.1 2.7

For the MBDC format % sum to 100 within rows, within years.

92.0 91.3 95.4 80.0 68.2 40.9 56.5 14.3 19.1

2.2 1.1 0.0 13.0 15.2 13.0 9.7 1.1 10.1 1.1 22.3 3.3 6.5

178

WELSH AND POE

PC responses reach a mode at $10 and are positively skewed. Response spikes are found at obvious rounded thresholds Že.g., $10 and $100.. Similarly, the distribution of MBDC responses follow expected patterns. The proportion of ‘‘Definitely Yes’’ responses decreases, and the proportion of ‘‘Definitely No’’ responses increases, monotonically with threshold values. ‘‘Probably Yes’’, ‘‘Not Sure’’, and ‘‘Probably No’’ responses peak at intermediate values. The OE values exhibit a positive skew with an observable modal pattern at rounded thresholds, most notably $100. Estimation of PC, DC, and OE response functions and the ‘‘Definitely Yes’’, ‘‘Probably Yes’’, and ‘‘Not Sure’’ MBDC switching functions used the boundedlikelihood function in Eq. Ž1., and the standard logistic function for the cumulative distribution function

FŽ X; ␤ . s

1 yŽ ␣ q ␤ X .

1qe

.

Ž 3.

As shown in Table II, the estimated constant Ž ␣ . and slope Ž ␤ . coefficients in each model were significant at the 5% level. Also the relative precision, defined here as the coefficient of variation, of the single bounded DC estimates is much lower than the corresponding MBDC counterparts. This result is consistent with past comparisons of single and multiple bounded formats w33, 15x. The corresponding logit models are graphically depicted in Fig. 3. Within the MBDC format, the estimated distributions shift to the right with a decline in the level of voting certainty. That is to say, the estimated logit function corresponding to the ‘‘Prob-

TABLE II Estimated Logit Models a, b

␣

Def. Yes, MBDC Prob. Yes, MBDC Not Sure, MBDC Payment card Dichotomous choice Open ended a

␤

n

1994

1995

1994

1995

1994

1995

1.048 Ž0.136.*** 1.426 Ž0.146.*** 1.572 Ž0.154.*** 1.404 Ž0.143.*** 1.806 Ž0.249.***

1.069 Ž0.183.*** 1.458 Ž0.204.*** 1.736 Ž0.223.***

y0.080 Ž0.005.*** y0.041 Ž0.003.*** y0.019 Ž0.001.*** y0.044 Ž0.003.*** y0.020 Ž0.003.***

y0.071 Ž0.007.*** y0.035 Ž0.003.*** y0.021 Ž0.002.***

185

96

185

96

185

96

1.400 Ž0.207.***

188 204 y0.030 Ž0.003.***

92

*** Denotes 1% significance level. Using likelihood ratio tests, the payment card and probably yes models Ž1994. were not significantly different ŽLR s 0.93., the open ended and probably yes models Ž1995. were not significantly different ŽLR s 1.51., the dichotomous choice and not sure models Ž1994. were not significantly different ŽLR s 0.95. at the 5 percent significance level. The null hypothesis of equality was rejected for all other 2 models Ž ␹ 0.052 s 5.99.. b

MULTIPLE BOUNDED DISCRETE CHOICE

179

FIG. 3. Estimated logit distributions. Ža. 1994 MBDC, DC and PC; Žb. 1995 MBDC and OE.

ably Yes’’ coding of the MBDC data lies to the right of the estimated logit function corresponding to the ‘‘Definitely Yes’’ coding of the MBDC data. The graphical depiction also indicates that there is a close correspondence between the DC and the ‘‘Not Sure’’ MBDCŽ1994. model, and the PC and ‘‘Probably Yes’’ MBDCŽ1994. model. For the 1995 data, there is a close correspondence between the estimated OE valuation function and the ‘‘Probably Yes’’ MBDCŽ1995. estimate. Statistical equivalence of the different logit models was evaluated with the following hypothesis test: H 1 : F Ž X ; ␤1 . s F Ž X ; ␤ 2 . . Of the 16 possible within year pairwise hypothesis tests, only F Ž X; ␤ PC . s F Ž X; ␤ Prob. Yes, MBDCŽ1994. ., F Ž X; ␤OE . s F Ž X; ␤ Prob. Yes, MBDCŽ1995. ., and F Ž X; ␤ DC .

180

WELSH AND POE

s F Ž X; ␤ Not Sure, MBDCŽ1994. . were not rejected at the 5% level using the likelihood ratio test in Eq. Ž2.. All other comparisons were rejected. These results suggest that individuals who are unsure about their WTP as indicated by responses to a specified dollar threshold in the MBDC format, would respond ‘‘Yes’’ to a similar dollar threshold presented in a DC format. Such an interpretation conflicts with the Ready et al. w26x polychotomous choice analysis that DC respondents switch from ‘‘Yes’’ to ‘‘No’’ responses close to the lower bound of the so-called ‘‘ambivalence region’’,6 but is consistent with past research indicating yea-saying and overstatement in DC and other posted offer markets w17, 20, 29x. In contrast, the estimated PC and OE response functions exhibit patterns similar to that of the ‘‘Probably Yes’’ MBDCŽ1994. and the ‘‘Probably Yes’’ MBDCŽ1995. models, respectively. This result suggests that respondents to the PC and OE formats are fairly certain about their WTP statements. This result is consistent with the DuBourg et al. w11x finding that continuous WTP responses tend to lie at the lower end of an individual’s value distribution. For each model the analytical median Žy␣r␤ . and the nonnegative ŽNN. mean ŽylnŽ1 q exp ␣ .r␤ . values of WTP were calculated from the parameter estimates, and 95% confidence bounds were estimated using the Krinsky and Robb parametric bootstrap procedure w24x. Summaries for statistics of the bootstrapped distributions are shown in Table III. Comparisons of these distributions reveal patterns consistent with the results of the likelihood ratio tests of H 1. There is a substantial degree of overlap between the following pairs of bootstrapped distributions: PC and the ‘‘Probably Yes’’ MBDCŽ1994. model, OE and the ‘‘Probably Yes’’ MBDCŽ1995. model, DC and ‘‘Not Sure’’ MBDCŽ1994. model. As expected from the comparative efficiency of single and multiple bounded models, the DC model had a much wider dispersion than the MBDC counterpart. Difference of means and median tests were conducted for each of the 16 possible within-year comparisons using the convolutions approach developed in Poe et al. w25x. Hypotheses of equality were not rejected for the PCr‘‘Probably Yes’’ MBDCŽ1994., the OEr‘‘Probably Yes’’ MBDCŽ1995., and the DCr‘‘Not Sure’’ MBDCŽ1994. mean and median comparisons. All other pairwise comparisons were rejected at the 5% level. Importantly, the disparity between DC and PC formats is significant and large, a result consistent with other studies comparing these two formats. Estimated 95% confidence bounds do not overlap, and DCrPC ratios for the mean and median are 2.7 : 1 and 2.9 : 1, respectively, which fall in the range of past DCrPC and DCrOE ratios observed in other studies w13, 27x. Direct comparison of the PC and DC values with the OE values is, however, not possible due to the assumed shift in underlying values across years. Yet, because both are statistically equal to the The Ready et al. w26x results may be attributed to the arbitrary definition of ‘‘ambivalence zone’’ bounds. Their polychotomous choice format included six response options related to the direction and strength of preferences between the reference and target condition, but did not include an ‘‘Unsure’’ response option. Instead, the lower bound of the ambivalence zone was defined as the lowest dollar amount to which 50% of the respondents would respond ‘‘Probably No’’ or ‘‘Definitely No’’. The upper bound was the highest dollar amount to which 50% would give a ‘‘Probably Yes’’ or a ‘‘Definitely Yes’’ response. The middle of the ambivalence region was defined as the dollar value at which 50% of the respondents would say ‘‘Maybe Yes’’ or higher. In three studies investigated, DC responses fell below the middle of this arbitrary ambivalence region. 6

181

MULTIPLE BOUNDED DISCRETE CHOICE TABLE III Krinsky and Robb Simulation Values for Median Žy␣r␤ . and Mean of Nonnegative Distribution a Median at Parameters w95% CIx

Def. Yes, MBDC Prob. Yes, MBDC Not Sure, MBDC Payment card Dichotomous choice Open ended

NN Mean at Parameters w95% CIx

1994

1995

1994

1995

12.96 w9.92, 16.34x 34.38 w28.87, 39.80x 82.96 w70.05, 96.91x 31.69 w26.02, 37.18x 90.76 w72.38, 112.38x

15.14 w10.53, 20.04x 41.80 w32.51, 52.39x 82.74 w65.51, 99.65x

16.70 w14.33, 19.51x 39.56 w34.62, 44.40x 92.96 w81.10, 106.15x 36.64 w32.05, 41.64x 98.40 w81.56, 123.86x

19.32 w15.80, 23.89x 47.80 w40.18, 57.80x 90.00 w76.32, 107.33x

46.47 w34.50, 57.88x

53.79 w44.07, 63.96x

a

Convolutions significance Ž ␨ . of difference: DCᎏNot Sure MBDCŽ1994. Median ␨ s 0.53, NN Mean ␨ s 0.66; Prob. Yes, MBDCŽ1994. ᎏPC Median ␨ s 0.55, NN Mean ␨ s 0.45; OEᎏProb. Yes, MBDCŽ1995. Median ␨ s 0.55, NN Mean ␨ s 0.38. All other combinations did not overlap, and the distribution of the convolution did not include zero. This leads to a rejection of the null hypothesis.

‘‘Probably Yes’’ MBDC model in their respective years, it appears that both invoke similar average response functions. 5. SUMMARY AND CONCLUSIONS This paper supports the findings of previous research that the choice of elicitation method can significantly influence estimates of mean and median WTP in contingent valuation studies. Based on the results of this study, at least part of the observed elicitation effect may be attributed to how participants respond to each elicitation format under the assumption that respondents have a distribution of values. The MBDC model presented in this paper allows respondents to express how certain they are that they would vote yes or no in a referendum to provide a public nonmarket good at a range of prices. The results indicate that inferences consistent with three widely used elicitation techniquesᎏopen-ended, payment card, and dichotomous choiceᎏfall within the range of MBDC estimates and might be obtained as special cases of the MBDC technique. A comparison between the MBDC technique and the dichotomous choice technique suggests that, all else equal, when respondents to a single dichotomous choice question are unsure whether they would pay the dollar threshold, they are likely to report they would vote ‘‘Yes’’. In contrast, both the open-ended and the payment card techniques elicit WTP measures that are consistent with a higher level of certainty. The correspondence between a range of elicitation techniques and various formulations of the MBDC model suggests that the MBDC model may provide a useful technique in light of the current controversy over contingent valuation of passive use values. Notably, the NOAA panel w2x concluded that contingent

182

WELSH AND POE

valuation studies should be based on the single bounded dichotomous choice technique as the discrete choice context closely resembles familiar market and voting decisions. However, many researchers have expressed concerns about this recommendation. First, some researchers worry about the potential for the dichotomous choice technique to result in overestimates of mean WTP w4, 29x. Second, the use of the single bounded dichotomous choice technique requires the researcher to choose a distribution of dollar offers. Selecting dichotomous choice offers is a difficult task at best, and an inefficient set of offers may impact estimates of mean WTP w19, 20x. Finally, the dichotomous choice technique, all else equal, provides less statistical information per observation than other elicitation techniques. The multiple bounded technique offers the opportunity to preserve a discrete choice questioning format, while also allowing the researcher to estimate a variety of mean WTP values that, based on the results of this study, approximate estimates that would be obtained using other elicitation techniques. Furthermore, while maintaining the discrete choice format, the multiple bounded approach provides higher levels of precision and at the same time avoids many of the difficulties associated with the choice of offers required to implement either a single bounded or double bounded model. While we believe the MBDC format offers many practical advantages, application of this method may leave the researcher in a quandary as to which of the alternative MBDC measures of value are most appropriate for use in policy analysis. Several strategies could be used to address this issue. First, examining the range of value estimates may provide sufficient information for decision making. For example, if the benefits of a policy, as measured by the value associated with the ‘‘Definitely Yes’’ model, exceed the costs of the policy, it is fairly clear that the policy would pass a benefit cost test. Likewise, if the costs of the policy exceed the benefits, as measured by the values associated with the ‘‘Not Sure’’ model, the policy is unlikely to pass a benefit cost test. As an alternative, one might choose the appropriate MBDC model based on the consequences associated with errors in estimating benefits. Adopting this perspective, valuation estimates might be based on the ‘‘Definitely Yes’’ model if there are severe consequences associated with overestimating benefits and mild consequences associated with underestimating benefits. The choice of a preferred MBDC value estimate could also be guided by the results of literature assessing the validity of contingent valuation. For example, a recent study of road removal from areas on the north rim of the Grand Canyon w8x found that respondents to a DC question who were most certain about their response, had a mean WTP approximating that revealed by the behavior of individuals actually solicited to contribute to this program. This indicates that contingent values expressed with a higher degree of certainty might be more valid measures of actual WTP. In terms of the MBDC model, this result suggests that the ‘‘Definitely Yes’’ model may be most appropriate. Finally, we acknowledge that more sophisticated ways of modeling certainty levels will almost certainly be developed with likely emphasis on modeling uncertainty at each referendum dollar threshold and providing a single estimate of WTP. Že.g., w7, 1x.. Thus, while the choice of value measure raises some issues, the above suggestions offer ways to address these issues. Furthermore, we believe the problems of dealing with the issue of multiple value estimates are more than offset by other advantages of the MBDC method.

183

MULTIPLE BOUNDED DISCRETE CHOICE

APPENDIX Dichotomous Choice Format Would you vote for this proposal if passage of the proposal would cost you $ every year for the foreseeable future Ž CIRCLE ONE NUMBER. 1. No 2. Yes Payment Card Format If the passage of the proposal would cost you these amounts every year for the foreseeable future, what is the highest amount you would pay and still vote for the program? Ž CIRCLE THE HIGHEST AMOUNT THAT YOU WOULD STILL VOTE FOR THE PROGRAM . 10¢ $30 $200

50¢ $1 $5 $40 $50 $75 MORE THAN $200

$10 $100

$20 $150

Open Ended Format If passage of the proposal would cost you some amount of money every year for the foreseeable future, what is the highest amount that you would pay annually and still vote for the program? ŽWRITE IN THE HIGHEST DOLLAR AMOUNT AT WHICH YOU WOULD STILL VOTE FOR THE PROGRAM . $ REFERENCES 1. A. Alberini, K. J. Boyle, and M. P. Welsh, Using multiple bounded questions to incorporate preference uncertainty in non-market valuation, in ‘‘W-133, Benefit and Cost Transfers in Natural Resource Planning,’’ 9 th Interim Report, University of Nevada, Reno Ž1997.. 2. K. Arrow, R. Solow, E. Leamer, P. Portney, R. Randner, and H. Schuman, Report of the NOAA Panel on Contingent Valuation, Appendix I, Federal Register 58, 4602᎐4603 Ž1993.. 3. K. J. Boyle, F. R. Johnson, D. W. McCollum, W. H. Desvousges, R. W. Dunford, and S. P. Hudson, Valuing public goods: Discrete versus continuous contingent-valuation responses, Land Econom. 72, 381᎐396 Ž1996.. 4. T. Brown, P. Champ, R. Bishop, and D. McCollum, Which response format reveals the truth about donations to a public good?, Land Econom. 72, 152᎐166 Ž1996.. 5. T. A. Cameron and D. D. Huppert, OLS versus ML estimation of non-market resource values with payment card interval data, J. En¨ iron. Econom. Management 17, 230᎐246 Ž1989.. 6. T. A. Cameron and J. Quiggin, Estimation using contingent valuation data from a dichotomous choice with follow-up questionnaire, J. En¨ iron. Econom. Management 27, 218᎐34 Ž1994.. 7. T. A. Cameron, G. L. Poe, R. G. Ethier, and W. D. Schulze, ‘‘A Comparison of Alternative CV Elicitation Methods with Actual Contributions,’’ selected AERE paper presented at the ASSA meetings, Chicago Ž1998.. 8. P. A. Champ, R. C. Bishop, T. C. Brown, and D. W. McCollum, Using donation mechanisms to value nonuse benefits from public goods,’’ J. En¨ iron. Econom. Management 33, 151᎐163 Ž1997..

184

WELSH AND POE

9. R. C. Cummings, D. S. Brookshire, and W. D. Schulze ŽEds.., ‘‘Valuing Environmental Goods: An Assessment of the Contingent Valuation Method,’’ Rowan & Allanheld, Totowa, NJ Ž1986.. 10. W. Desvousges, F. R. Johnson, R. W. Dunford, K. J. Boyle, S. P. Hudson and K. N. Wilson, ‘‘Measuring Nonuse Damages Using Contingent Valuation: An Experimental Evaluation of Accuracy,’’ Research Triangle Institute Monograph 92-1, Exxon Corporation Ž1992.. 11. W. R. DuBourg, M. W. Jones-Lee, and G. Loomes, Imprecise preferences and the WTP-WTA disparity, J. Risk Uncertainty 9, 115᎐133 Ž1994.. 12. D. M. Grether and C. R. Plott, Economic theory of choice and the preference reversal phenomenon, Amer. Econom. Re¨ . 69, 623᎐638 Ž1979.. 13. M. Haefele, R. A. Kramer, and T. Holmes, Estimating the total value of forest quality in high-elevation spruce-fir forests, in ‘‘The Economic Value of Wilderness,’’ General Technical Report SE-78, Southern Forest Experiment Station, Research Triangle Park, NC Ž1992.. 14. W. M. Hanemann, Welfare evaluation in contingent valuation experiments with discrete responses, Amer. J. Agr. Econom. 66, 332᎐341 Ž1984.. 15. W. M. Hanemann, J. Loomis, and B. Kanninen, Statistical efficiency of double-bounded dichotomous choice contingent valuation, Amer. J. of Agr. Econom. 72, 1255᎐1263 Ž1991.. 16. J. P. Hoehn and A. Randall, A satisfactory benefit cost indicator from contingent valuation, J. En¨ iron. Econom. Management 14, 226᎐247 Ž1987.. 17. T. P. Holmes and R. A. Kramer, An independent sample test of yea-saying and starting point bias in dichotomous-choice contingent valuation, J. En¨ iron. Econom. Management 29, 121᎐132 Ž1995.. 18. J. Jackson, Structural characteristics of norms, in ‘‘Current Studies in Social Psychology’’ ŽI. D. Stein and M. Fishbein, Eds.., Holt, Reinhart and Winston, New York, 301᎐309 Ž1965.. 19. B. J. Kanninen, Design of sequential experiments for contingent valuation studies, J. En¨ ironm. Econom. Management 25, S-1-11 Ž1993.. 20. B. J. Kanninen, Bias in discrete response contingent valuation, J. En¨ ironm. Econom. Management 28, 114᎐125 Ž1995.. 21. C.-Z. Li and L. Mattson, Discrete choice under preference uncertainty: An improved structural model for contingent valuation, J. En¨ ironm. Econom. Management 28, 256᎐269 Ž1995.. 22. D. McFadden, Contingent valuation and social choice, Amer. J. Agr. Econom. 76, 689᎐708 Ž1994.. 23. J. J. Opaluch and K. Segerson, Rational Roots of ‘Irrational’ Behavior: New Theories of Economic Decision-Making, Northeastern J. Agr. Resour. Econom. 18, 81᎐95 Ž1989.. 24. T. Park, J. B. Loomis, and M. Creel, Confidence intervals for evaluating benefits estimates from dichotomous choice contingent valuation studies, Land Econom. 67, 64᎐73 Ž1991.. 25. G. L. Poe, E. K. Severance-Lossin, and M. P. Welsh, Measuring the difference Ž X-Y . of simulated distributions: A convolutions approach, Amer. J. Agr. Econom. 76, 904᎐915 Ž1994.. 26. R. C. Ready, J. C. Whitehead, and G. C. Bloomquist, Contingent valuation when respondents are ambivalent, J. En¨ ironm. Econom. Management 29, 181᎐196 Ž1995.. 27. R. C. Ready, J. C. Buzby, and D. Hu, Differences between continuous and discrete contingent value estimates, Land Econom. 72, 397᎐411 Ž1996.. 28. D. A. Schkade and J. W. Payne, Where do the numbers come from? How people respond to contingent valuation questions, in ‘‘Contingent Valuation: A Critical Assessment’’ ŽJ. A. Hausman, Ed.., North Holland, New York, 271᎐293 Ž1993.. 29. W. Schulze, G. McClelland, D. Waldman, and J. Lazo, Source of bias in contingent valuation, in ‘‘The Contingent Valuation of Environmental Resources: Methodological Methods and Research Needs’’ ŽD. J. Bjornstad and J. R. Kahn, Eds.., Edmund Elger, Cheltenham, UK Ž1996.. 30. B. Shelby, Encounter norms in backcountry settings: Studies of three rivers, J. Leis. Res. 13, 129᎐138 Ž1981.. 31. B. Shelby, T. C. Brown, and R. Baumgartner, Effects of streamflows on river trips on the Colorado River in the Grand Canyon, Arizona, Ri¨ ers 3, 191᎐201 Ž1992.. 32. P. Slovic and S. Lichtenstein, Preference reversals: A broader perspective, Amer. Econ. Re¨ . 73, 596᎐605 Ž1983.. 33. M. P. Welsh and R. C. Bishop, Multiple bounded discrete choice models, in ‘‘Benefits & Costs Transfer in Natural Resource Planning’’ ŽJohn Bergstrom, Ed.., Western Regional Research Publication, W-133, Sixth Interim Report, Department of Agricultural and Applied Economics, University of Georgia, 331᎐352 ŽSept. 1993..

MULTIPLE BOUNDED DISCRETE CHOICE

185

34. M. P. Welsh, R. C. Bishop, R. M. Baumgartner, and M. L. Phillips, ‘‘Pilot Test, Non-Use Value Study, Glen Canyon Environmental Studies: Final Report,’’ Report to Glen Canyon Environmental Studies, U.S. Bureau of Reclamation, HBRS Inc., Madison Ž1994.. 35. M. P. Welsh, R. C. Bishop, M. L. Phillips, and R. M. Baumgartner, ‘‘GCES Non-Use Value Qualitative Research: Final Report,’’ A report to Glen Canyon Environmental Studies, U.S. Bureau of Reclamation, Hagler Bailly Consulting Inc., Madison Ž1995a.. 36. M. P. Welsh, R. C. Bishop, M. L. Phillips, and R. M. Baumgartner, ‘‘GCES Non-Use Value Study: Final Report,’’ Report to Glen Canyon Environmental Studies, U.S. Bureau of Reclamation, Hagler Bailly Consulting Inc., Madison Ž1995b..