The Case for Diminishing Marginal Existence Values1

Ž .JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 36, 324]344 1998ARTICLE NO. EE981045

The Case for Diminishing Marginal Existence Values1

Kimberly Rollins

Department of Agricultural Economics and Business, Uni ersity of Guelph, Guelph, Ontario,Canada, N1G 2W1

and

Audrey Lyke

Database Analyst, PNC Bank, Wilmington, Delaware

Received August 12, 1997; revised June 30, 1998

This study addresses the debate over sensitivity of existence values measured by contingentvaluation to scope tests. We reconcile much of the debate within one theoretical model. Ifmarginal WTP for existence goods is diminishing, then a study that tested for sensitivity toscope over a range for which marginal WTP is high would be more likely to detect sensitivityto scope than a study that focused on a range for which marginal WTP is much lower. Anempirical model demonstrates this point for existence value of remote wilderness parks.These results have significant implications for future contingent valuation work. Q 1998

Academic Press

I. INTRODUCTION

This article contributes to the debate over the use of contingent valuation tomeasure existence values. In the debates over environmental damage assessment,there has been much disagreement over the extent to which nonusers of a

w xcompromised resource suffer economic damages 15, 26, 3, 7 . The sensitivity ofmeasured existence values to changes in the size of scope of the good has been

w xcalled into question 2, 4, 9, 22 . A number of studies have investigated the issue ofw xinsensitivity to scope 18, 6, 27, 28, 24 , conducting empirical tests and proposing

theoretical explanations. Much of the empirical literature focuses on whether orŽ .not existence values as estimated by contingent valuation CV are sensitive to the

w xscope of the existence good in question 4, 6, 7, 28 . For example, in a study ofw xmigratory waterfowl deaths, Boyle et al. 4 found insensitivity to scope of migratory

waterfowl deaths for 2% or less of waterfowl populations, and recommendedfurther research to investigate the measurement of the value of small changes inthe provision of environmental goods.

Much of the literature that interprets the implications of the debate do so interms of the reliability of CV to measure existence values. Diamond and Hausman

1 The authors wish to gratefully acknowledge the support of Parks Canada and the Richard IveyFoundation of Ontario. We also wish to acknowledge the important contributions of Daniel Rondeau,Caroline Gunning-Trant, Wolfgang Haider, and two anonymous referees. Any remaining errors are ourown responsibility.

3240095-0696r98 $25.00Copyright Q 1998 by Academic PressAll rights of reproduction in any form reserved.

MARGINAL EXISTENCE VALUES AND SCOPE 325

w x10 review a number of CV studies that are not sensitive to scope and theyconclude that because individuals may not be able to distinguish between goods ofdifferent scope, reliability of CV estimates of existence values are suspect. In theirstudy of the value of the 49th and 50th parks out of a system of 57 wilderness

w xparks, McFadden and Leonard 22 conclude that CV estimates are not sensitive tow xscope in the case of unfamiliar and remote wilderness areas. Carson 6 reviews

over 30 tests in which CV estimates are sensitive to scope and he concludes thatCV can produce reliable estimates in well constructed studies. Smith and Osbornew x28 used a meta-analysis of past CV studies to conclude that estimates of thevalues of changes in visibility are sensitive to scope, and that similar analysis couldbe used to determine the reliability of existence values for other goods.

A number of articles have been concerned with how to devise various ‘‘tests ofscope’’ that any CV study must pass in order for the estimates to be regarded as

w x w xreliable 2, 9 . Diamond 9 proposed a simple test of scope in which the ratio ofŽ .two willingness to pay WTP estimates for two different levels of scope should be

greater than the ratio of the differences in size of the existence good. Smith andw xOsborne 28 questioned whether it is a reasonable task to develop an unambigu-

ous test for scope, given the varying reasons for how changes in WTP may beassociated with changes in the scope of a good.

Upon reviewing the preceding studies, it seems to us that seemingly conflictingresults could all be reconciled within a simple theoretical framework, with implica-tions for the design of contingent valuation studies to measure existence values.The theory is very straightforward, following the familiar Okum’s razor principle ofnot using a more complicated theory when a simpler one will do. The empiricalwork was rather involved due to the number of internal consistency checks we builtinto the study.

We focus on the sensitivity of willingness to pay for successive quantities ofŽ .preservation. Willingness to pay WTP was estimated for proposals to create four

Ž .parks in Canada’s Northwest Territories NWT . Each park represents a uniqueCanadian ecosystem, and all were sufficiently remote that only 3% of the respon-dents who voted for park creation indicated they might some day visit them. Wethus postulate that the primary component of value being measured is existence orpassive use value.

The context of the empirical study was shared with the respondents via aninformation packet and maps. These materials explained that scientists described

Ž .Canada’s landscape as being comprised of 39 distinct natural regions NRs , andthat the National Parks System currently has representative examples of 29 ofthese NRs. A representative example is defined to be large enough to ensure thatthe ecological processes of the NR can continue if surrounding areas were to bedeveloped. The 10 NRs that are not yet represented in the National Parks Systemwere highlighted on maps included in the information packets. One of the 10 is onVancouver Island in British Columbia, five are in Northern Quebec and Labrador,

Ž .and four are in the Northwest Territories NWT . Canada’s National Parks Systemplan recommends completion of the Parks System by creating 10 parks that wouldincorporate representative examples of each of the remaining 10 NRs in Canada.

At the time the study was developed, Parks Canada developed proposals for fourspecific remote wilderness parks to be created in each of the four NRs in theNorthwest Territories. The empirical portion of this study is concerned with the

ROLLINS AND LYKE326

values of creating the four NWT parks and of completion of the parks system as awhole with representative examples of all 10 NRs. Thus the basic model considersthe completed parks system as the largest scoped good, which would include all39 NRs.2

In order to test for scope effects, we split the sample to include tests for thevalue of individual parks, pairs of parks, four parks, or 10 parks. For scope testsalone, there were nine versions of the survey instrument. In addition to the testsfor embedding and scope effects, we had several split-sample experiments to test:

Ž .the effects of question ordering, media effects phone-mail-phone versus mail-only ,double-bounded versus single-bounded dichotomous choice question format, levelof information provision, and donation to a foundation versus tax payment vehicle.The experimental design tested for differences in WTP among the four NWT NRsby further splitting the subsamples of respondents who received one-park onlyversions and those who received two-park only versions of the mail-only survey.3

Ultimately, not including a parallel discrete choice experiment study that wasconducted concurrently, there were over 50 versions of the survey instrument.Every version was available in French and in English. Phone interviews conductedin French were conducted by native French-speaking interviewers. For a descrip-

w xtion of the phone-mail-phone part of the research refer to Gunning-Trant 13 .The article is organized as follows. Section II develops the theoretical model of

diminishing marginal existence values. Section III describes the Northern Parksstudy and data. Section IV presents empirical results that show diminishingmarginal WTP. Section V describes the quality of the survey design, several testsfor internal consistency of the contingent valuation application, and their results.Implications are discussed in Section VI.

II. THEORY OF DIMINISHING MARGINAL EXISTENCE VALUES

In this section we first review the context in which we expect to find diminishingmarginal values for preserving additional wilderness areas. We note the circum-stances in which some work has contended that, conversely, WTP may be expectedto be convex and we explain where our study differs. We suggest a frameworkwhich is consistent with the seemingly disparate results of various empirical scopetests in the literature.

2 Each NR is, by definition, in a different region of Canada. The good that respondents were askedto value was not the total acreage protected, but rather the number of NRs that the Parks System would

Žcontain, out of a total of 39 given that each park was of size sufficient to preserve ecological functions.of the NR it was meant to represent . The information each survey participant received included, among

many other things, the size of each proposed new park. Park sizes among the four NWT proposed parksdid not vary by a great amount; all four were extremely large, measured as thousands of km2.

3 w xDiamond 9 suggested that ‘‘any CV survey claiming to measure true WTP should be able to varythe scenario in order to’’ perform internal consistency tests to determine whether the results conform toeconomic theory. He declares that ‘‘until we have a larger body of surveys with internal consistencytests, people will disagree about the chances of success of future CV surveys that try to measure nonusevalues. Having theory spelled out explicitly helps describe the internal consistency checks that can beused to evaluate particular surveys.’’ Thus, it is in this general spirit that the research described in thisarticle set out to develop an experimental design that allowed testing of the hypotheses that existencevalues for environmental goods can be subject to diminishing marginal returns, and that this phe-nomenon may explain the failure of many other surveys to pass so-called ‘‘scope tests.’’


Our empirical work was conducted in the context of a proposed public policythat would preserve representative examples of distinct natural regions by estab-lishing parks with high levels of protection. Respondents were told the context,which is that biologists identified 39 distinct ecological regions in Canada, that 29of these regions contained at least one national park, and that 10 did not. We

Ž .investigated the value of representing more regions 1, 2, 4, and 10 with parks.If preferences for existence goods are well-behaved, then, as more of the

existence good is provided, measured existence values should be consistent withtwo economics principles: nonsatiation and diminishing marginal value. In thecontext of expenditure functions, we briefly review the results that WTP increasesas the scope of the good increases, but the marginal WTP decreases as more of thegood is offered to the consumer. Due to diminishing marginal WTP, a thirdprinciple comes into play: when measurement is inexact, it is more difficult todetect a small difference than a large difference. Taken together, these principleshave implications, discussed later in this article, for the design of experiments tomeasure WTP for existence goods.

Ž .Let e p, y, u denote the expenditure function to achieve maximum utility u,Žgiven base level y of the public good and where p is the numeraire price of all

.other goods . Let D y denote the change in the level of the public good. In ourempirical example, y represents the 29 regions already represented in the park

Žsystem, and D y represents the additional number of regions to be represented 1,.2, 4, or 10 . The properties of WTP are then derived from the expenditure function

as follows:4

WTP D y s e p , y , u y e p , y q D y , u , 1Ž . Ž . Ž . Ž .

WTP D y y e p , y q D y , uŽ . Ž .s . 2Ž .

y y

w x Ž .Maler 21 established that the RHS expression in Eq. 2 is the utility-constant¨marginal value, or virtual price p¨.

WTP D y y e p , y q D y , uŽ . Ž .¨s s p p , y q D y , u . 3Ž . Ž .

y y

The virtual price is positive, so the WTP for each additional region to berepresented should be positive.

The second derivative of WTP will equal the derivative of the virtual price withw xrespect to D y. In the case of a single good, Madden 19 shows that this derivative

is always strictly negative for strictly convex preferences. Thus WTP increases, butat a decreasing rate. We should observe diminishing marginal existence values.

4 An earlier version of this article modeled this problem as its dual, using the indirect utility function.We thank an anonymous referee for pointing out the greater simplicity of the expenditure functionapproach.

ROLLINS AND LYKE328

However, as the number of natural regions to be represented within the parkssystem increases, the marginal WTP for an additional region represented shoulddiminish.5 In general, as a population or protected area reaches maximum size,each increment is worth less and hence it will be more difficult to pass the types ofscope tests which are discussed in the literature.

Suppose a study, Study I, was designed to estimate WTP for subunits of differingscope for a good in the lower region of the WTP curve shown in Figure 1.Meanwhile another study, Study II, was designed to estimate WTP for differentscoped units of the same good in the upper region of the same WTP curve. Study Imight determine WTP for a program to create two parks, three parks, and fourparks, for example; while Study II might determine WTP for eight parks, nineparks, and all ten parks. We can further imagine that, except for the scope of the

Žgood, all other elements of the studies are identical payment vehicles, information,.CVM elicitation format, sample design, sample size .

It is feasible that Study II results might indicate no measurable difference inWTP between subunits of different scope. Meanwhile Study I, which uses subunitsof the same difference in scope as those in Study II, but along a different section ofthe WTP curve, would theoretically result in a much greater difference in WTP.

5 w xMajid, Sinden, and Randall 20 demonstrated declining WTP from the viewpoint of substitutioneffects for systems of generically similar public goods. They also used a system of parks as an empiricalexample. ‘‘When each proposed park can reasonably be considered one-of-a-kind, the benefit evalua-tion question quite properly is: ‘‘What is the total benefit of a given area of land as a park?’’. . . However, as the . . . facilities development programs continue, the valuation question becomes:‘‘What is the marginal value of a given area of land as an increment to an existing park system?’’ Theprior existence of a park system is recognized, and the traditional concerns of marginal analysis}for

Ž .example, diminishing marginal utility}come to the fore.’’ p. 377 . They pointed out that thesequestions had, in 1983, received little attention in the recreation literature. It seems that their commentcan be similarly applied to the CVM literature, and the debate about scope effects, of today.

FIG. 1. Diminishing marginal existence value.


Because the difference in value is so much smaller in Study II, a larger samplewould be required to detect a significant difference. For a given sample size thepower of the test is lower at the upper section of the WTP curve.

However, as stand alone studies, results of these two hypothetical studies mightappear to support conflicting interpretations as to whether respondents are able torespond to valuation questions regarding the good. One might conclude from StudyII that respondents do not have an ability to express economic values for existencegoods, that respondents cannot distinguish between goods of different scope, andthat contingent valuation is not useful, because existence values would appear tobe too fickle to be measurable. In direct contrast, one might conclude from Study Ithat people can respond to valuation questions about existence goods and that themeasured values appear to be consistent with economic theory.

One may interpret results as not passing a reliability test when in fact the issue isthat one does not know where the subunits of differing scope are positioned on thecurve. By using the same CV instrument and by varying the scope of the goodsufficiently, one can easily obtain results that would support the notion that bothsets of results, from Studies I and II, are fully consistent with one another and witheconomic theory. Thus, any CVM study that attempts to elicit existence valuesshould provide a minimum level of information that includes finite beginning andending points to the WTP curve in order to allow respondents to determine theappropriate level of scope.

III. AN EMPIRICAL EXAMPLE USING SUBSETS OF THE LARGESTSCOPED GOOD

Ž .The contingent valuation CV study consisted of two surveys: a mixed-modephone-mail-phone survey and a mail-only survey. The study was designed to controlfor as many differences as possible between the surveys except for CVM questionelicitation formats, with the mail-only being written and the mixed-mode beingverbal. All information that was not part of the CV questions was mailed to allparticipants in both surveys. Question order was the same for both formats, andevery attempt was made to keep wording as similar as possible for CV-relatedquestions. The mixed-mode survey was implemented during the months ofApril]May of 1995 and the mail-only survey was mailed out in August of 1995.

However, as much as was possible, the survey was designed to conform to theNOAA recommendations on survey design. Survey instruments and informationalmaterials were developed over a period of 2 years, with numerous focus groupsusing verbal protocol, pretests, and a pilot for each survey instrument. Theseextensive development efforts paid off in terms of respondent understanding of thetask, credibility of the scenario, response rates on general population surveysdealing with a remote and unfamiliar good, item response rates to the CVquestions, assurance that votes made full reference to program costs, and reason-able sensitivity to scope.

The Mixed-Mode Sur ey

Ž .The mixed-mode survey relied on random digit dialing RDD to make firstcontact with a random sample of Canadians. Respondents were interviewed, thenmailed a packet of information materials before being interviewed again. The first

ROLLINS AND LYKE330

interview gathered demographic data and the names and addresses of participants.The CV questionnaire was implemented during the second interview. Mixed-modeparticipants did not receive a written copy of the questionnaire; their mailingincluded only the informational materials, which described the proposals for thecreation of the new parks. The phone survey was implemented by professionalinterviewers at the Angus Reid Group, Canada’s foremost survey research firm.

The first interview asked a variety of attitudinal questions and questions de-signed to force respondents to make choices between a variety of alternative policyoptions with different economic implications. These questions were of a generalnature, to prepare respondents for the CV task; however, a specific focus onprotected areas was not revealed during the first interview to reduce response bias.Half of the first interview sample was randomly selected to receive a short test CVquestion on an unrelated subject. This test question was included to determine ifhaving had prior experience with the CV approach would in any way alter themagnitude or variance of these respondents’ answers to the subsequent new parksCV questions in the second interview. The prior question had no statisticallysignificant effect on the results reported in this article.

Mixed-mode participants were each asked two double-bounded dichotomouschoice referendum format valuation questions. One question was to vote on aproposal to create four specific parks in the NWT. These parks were individuallydescribed to respondents in the mailed information packets. The other questionwas to vote on a proposal to create all 10 parks as necessary to include representa-tive examples of each of the 39 Canadian NRs within the Parks System.

The question order was rotated so that 50% of the sample received the four-parkproposal first and 50% received the 10-park proposal first, so that ordering effectscould be tested. The mixed-mode respondents did not know in advance that theywould be asked about two separate park proposals. Thus, the 50% who answeredthe four-park question first did so not knowing that they would be asked to respondto a 10-park proposal, and vice versa. If respondents were merely motivated by aneed to ‘‘contribute to a good cause’’ without considering the scope of the good,then we would expect some indication of this in the resulting WTP estimates fromthe mixed-mode survey, such as little difference in WTP between the four-parkproposals and the 10-park proposals when they were each asked first in order. Inaddition, 50% of the sample was asked whether they would vote for each proposalif it were to cost their household nothing, before the double bounded bid ques-tions, in order to test for ‘‘yea-saying.’’

Of the initial 558 people contacted via RDD, 201 declined to be interviewed,leaving an initial response rate of 64%. Of the 357 contacts who agreed to

Ž . Žparticipate, 304 85% completed the second phone interview the period for the.second contact was limited to 1 week . Most of the remaining 15% were unavail-

able during the times that they had originally suggested they could complete the.interview . Item nonresponse rates for the phone CV questions were: 9.5% for the

four-park proposal and 8.2% for the 10-park proposal.

The Mail-Only Sur ey

The mail-only survey packet sent to participants consisted of the informationpages and a questionnaire. The mail-only questionnaires were divided into anumber of versions according to an experimental design that allowed for internal


consistency tests. Scope tests were conducted based on four levels of good provi-sion: one-park, two-park, four-park, and ten-park proposals. Table I describes the12 survey versions that were used for scope tests, simplifying by denoting the fourNWT parks as A, B, C, and D.

Sample sizes and response rates by version are listed in Table II. The 12 surveyversions used for this article accounted for a total of 1913 surveys mailed out to arandom sample of named Canadians over age 18, resulting in an overall responserate of 50.4%. The average item nonresponse rate to CV questions for themail-only survey instrument was 5.9%.

Informational Materials

Both CV instruments used the same set of informational materials. Informationpackets included 2 pages common to all versions, and combinations of up to fouradditional park-specific pages for park-specific versions. The common pages in-cluded maps and text describing the goal to complete the National Parks System bycreating parks that would each represent the 10 different Canadian ecologicalregions which are not yet represented in the current Parks system. A map ofCanada outlined all 39 ecological regions, indicated the 29 already represented inthe Parks System, and the 10 which remained to be represented.

The information packet included four individual pages with detailed maps anddescriptions of each of four specific proposed parks for the NWT. The informa-tional materials did not include individual descriptions of the six parks that werenot in the NWT; just a map showing the boundaries of the NRs that the other six

Ž .parks would represent. The mail-only sample included splits versions 1, 11, and 12that were designed to test for information effects, as explained in the resultssection in the following text.

The informational materials stressed that few visitors would ever visit theseremote northern parks due to the extreme expense. It was pointed out that becausethe purpose of these parks would be to preserve representative examples of

TABLE IMail-Only Survey Versions Used in Scope Tests

Survey versions Proposal I Proposal II

1 one park only Park A None2 one park only Park B None3 one and 10 parks Park A 10 parks4 one and 10 parks Park A 10 parks

with zero bid option5 one and 10 parks Park B 10 parks6 one and 10 parks Park B 10 parks

with zero bid option7 two and 10 parks Parks A q B 10 parks8 two and 10 parks Parks C q D 10 parks9 four and 10 parks Four parks 10 parks

10 four and 10 parks Four parks 10 parkswith zero bid option

11 four park only Four parks None12 10 park only 10 parks None

ROLLINS AND LYKE332

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Canada’s 39 Natural Regions, recreation opportunities for those who went wouldbe limited. Northern tundra ecosystems were described as being especially fragileand slow to recover from disturbance. For these reasons, the parks would not bedeveloped as tourist destinations, but instead as natural preserves, and no recre-ational infrastructure would be built by Parks Canada in these new parks.

The information discussed substitute uses of the areas, characterized in terms ofthe economic trade-offs. If parks were created, all exploration for mineral depositswould cease and the areas could never be used for mineral extraction, which couldprovide jobs and revenue for relatively poor northern communities. Mining is animportant source of NWT economic development.

Assessment of Respondents’ Understanding of Scenarios and Credibility of Scenarios

Repeated checks in the survey instrument indicated that the vast majority ofWTP responses are indicative of existence, not use values. These included ques-tions that asked whether they had ever or were likely to visit protected areas in theNWT. Follow-up questions to the CVM questions that asked why the respondentvoted ‘‘yes’’ or ‘‘no’’ included a number of questions that were meant to indicate

Žpossibility of use values. for example, ‘‘I voted for the proposal in case I might visitthese areas in the future,’’ ‘‘I voted for the proposal to protect the ecosystem for itsown sake,’’ ‘‘ I want to know that this area will continue to exist as it is,’’ and ‘‘Ivoted against the proposal because I would not be able to use the park myself.’’The conclusion that the WTP responses indicate existence values is extensively

w x.developed in Gunning-Trant 13 .Both the mixed-mode and the mail-only survey instruments included a section

that prompted respondents to be cognizant of their budget constraints, asked themto indicate from what category of discretionary funds they would make theirpayment, and to be aware of how the payment might affect their options for otheruses of the same funds. The categories of discretionary funds they were presentedincluded charitable donations.6 Both instruments allowed respondents to revisetheir answers in light of budget considerations. A few mixed-mode respondents didrevise their answers, and in those cases we used the revised bids.

A number of focus groups were conducted, both in English and in French. Thesurvey questionnaire and the informational materials were repeatedly revisedaccording to feedback received. The survey questionnaires were developed andpretested concurrently, with every attempt made to keep wording as similar aspossible between the phone-interview version and the written versions in themail-only survey. The survey was extensively pretested locally, then piloted once,sampling from the same population as the final version. The first pretests usedopen-ended CVM questions. The subsequent pretests used single-, and double-bounded formats. We used the double-bounded pretest results to select a biddesign for the pilot. The final version differed from the pilot only in a slightmodification of the bid design. The distribution that the bids were drawn from wasrepeatedly increased, little by little, with the heaviest weighting of bid values

6 Respondents who checked that they would pay for the parks with funds earmarked for charitabledonations were not, statistically, more likely to vote yes, or have higher WTP than those who did notcheck this category.

ROLLINS AND LYKE334

around the mean of the distribution. The final data set includes both the pilot andthe final version, and bid amounts ranged from $5 to $437.

In addition to evidence from focus groups, the survey included follow-up ques-tions after the CVM questions that were designed to determine whether therespondents felt the scenarios were credible. We had no reason to believe thatrespondents felt the scenarios were not credible. The scenarios used in the surveyare actual examples of proposed parks that have been under development forseveral years by Parks Canada. The process of new park creation involves specificsteps which, if the proposal is successful, finally culminate in an Act of Parliamentthat creates the park. All the four specific parks in the NWT described in thesurvey have progressed to the point at which the areas have been withdrawn fromany other uses until a final decision is made. All information provided in theinformational materials was developed with Parks Canada and accurately portrayedthe goal of the parks system to include all 39 natural regions and the four proposedparks.7 In terms of the scenario in which Parks Canada cannot pay for the newparks with existing program funds, the fact that the Parks budget has been cut byover 25% over the last few years is true, and most Canadians are painfully awarethat most government agencies are not able to fund new programs. The notion thatnew programs might be funded via a one-time earmarked surtax is not farfetched.The ‘‘surtax’’ is a common item on federal and provincial tax returns in the contextof other programs. Surtaxes are added as a separate line that is clearly identified.Thus the ability of the government to implement and to collect the fee is credible.

Double-Bounded Dichotomous Choice CV

The study employed a double-bounded dichotomous choice referendum questionformat with a one-time surtax as a payment vehicle.8 In a typical double-boundedformat, respondents are given a first question and a dollar amount to respond towith a yes or no answer. If the answer to the first question is no then the samequestion is posed, but with a lower dollar amount. Similarly, a yes answer to thefirst question is followed with a second question in which the dollar amount isincreased. The double-bounded format is well-suited for phone interviews, becausethe second questions and dollar amounts associated with them are hidden from therespondent. This procedure was used in the mixed-mode survey.

Written formats of double-bounded questions have relied on a series of ‘‘skippatterns’’ in the survey instrument which instruct participants to go to one versionor another of the follow-up question, based on the participant’s yes or no responseto the first question. No matter how elaborate the skip pattern, the alternativefollow-up questions are not hidden in a written format. It seemed to us that skippatterns and the additional space and complexity of the survey instrument weredistracting. Given that we had the mixed-mode survey for comparison of WTPestimates, we decided to use the simplest version of a double-bounded questionthat we could. The proposal was stated once, and the participant was asked to

7 Several respondents commented that they felt that the information was interesting and that theyenjoyed reviewing the materials.

8 The experimental design for the full study included single-bounded dichotomous choice andopen-ended formats as well, but these are not treated in this article. See Rollins, Lyke, and Gunning-

w xTrant 25 for a description of the full study design.


check yes or no based on each of two amounts posed. A sample of the wording ofone of the questions from the mail-only format is given in the Appendix.9

It has been shown that the follow-up question substantially increases theefficiency of WTP estimates over those obtained from single-bounded formatsw x14, 1 . The double-bounded approach was chosen for this study because it wouldallow more testing which involved partitioning the data for a given sample size. Atthe time that the study was developed, there was concern that the follow-upquestions posed in double-bounded procedures elicited a second WTP value fromrespondents that was correlated with the first, but not necessarily identical as the

w xfirst 5 , and assuming that the two values were identical could result in biasedestimates. That is, the responses to the second amounts posed may be influencedby the first amount, as well as by the actual WTP for the good. For this reason, thesample was split and versions of the mail survey were created with single-boundeddichotomous choice questions in order to determine if there was an indication of

w xany bias. Alberini 1 has since demonstrated that the bias is not large. In the caseof this study, the gain in efficiency allowed a number of additional tests, such asthose reported in this article, which would not have been possible given the samenumber of single-bounded responses.10

w xCooper and Hellerstein’s 8 CVM double-bounded logit routine was used forthe estimation. The routine uses maximum likelihood estimation and the analytical

w xmodel developed by Hanneman, Loomis, and Kanninen 14 . Confidence intervalsw xaround the WTP point estimates are calculated using the Krinsky and Robb 16

method.

IV. EMPIRICAL RESULTS

The data from this study conform to the theoretical model which implies thatmean household WTP is increasing in the number of parks, and marginal WTP perhousehold is decreasing in the number of parks. Using the mail survey, the meanWTP per household estimated for one park was $105.45, $161.85 for two parks,$191.57 for four parks, and $188.44 for 10 parks. Table III shows the coefficientsand the confidence intervals in addition to these point estimates. Table IVsummarizes mixed-mode results, in which the mean WTP was $235.18 for fourparks and $261.51 for 10 parks.

Figure 2 illustrates WTP versus number of parks; the ‘‘curve’’ is clearly increas-ing and concave, except that the difference between WTP for four parks and WTPfor 10 parks is insignificant. One explanation for this would be that after four parkshave already been created the consumer is nearing satiation and marginal WTP isvery low.

Marginal WTP was computed from the total WTP estimates where possible.Figure 3 shows the way marginal WTP diminished. The marginal value of the firstpark is equivalent to the value for one park, estimated at $105.45. Subtracting WTPfor one park from WTP for two parks, a point estimate for the marginal WTP for a

9 Copies of survey materials, including the informational materials, phone interview scripts, andmail-only questionnaires are available from the authors.

10 In designing the study reported here, we chose to send to a subsample of our sample, a version ofthe mail-only survey which used a single-bounded logit format, so that we could determine whether thesingle bounded estimates were different from the double-bounded estimates.

ROLLINS AND LYKE336

TABLE IIICVM Mail Results: WTP per Household

All one-park All two-park All four-park All 10-parkresponses responses responses responsescombined combined combined combined

Constant 0.54 y0.30 1.66 0.28Ž . Ž . Ž . Ž . Ž .t-value 0.97 y0.34 8.105 0.69

Ž .Bid amount $ y0.02 y0.01 y0.01 y0.01Ž . Ž . Ž . Ž .y10.04 y7.82 y9.96 y16.33

aŽ .Education years 0.11 0.07Ž . Ž .2.13 2.95

aŽ .Age years 0.02Ž .1.97

Disagree with goal y2.24 y1.46 y1.64 y1.88Ž . Ž . Ž . Ž . Ž .1 s yes; 0 s no y4.92 y2.94 y3.76 y7.06

N 266 173 256 730Log-likelihood y257.67 y196.41 y272.47 y762.08WTP estimate $105.45 $161.85 $191.57 $188.4495% c.i. for WTP $93.16]$119.72 $137.01]$190.27 $169.01]$220.43 $173.68]$205.74

aVariables which proved to be statistically not significant, such as household income, age, andeducation, were omitted from valuation functions. Thus ‘‘age’’ was included only for the one-parkresponses because it was not significant in the other valuation functions.

Žsecond park is $56.40. Marginal WTP equal to $29.72 for two more parks the third.and fourth is found by subtracting WTP for two parks from WTP for four parks,

so that the average WTP for each of these parks is $14.86. For mail surveyŽestimates, adding six more parks after four were created is not significant ap-

.parently worth a loss of $3.13 . The marginal WTP for the six more parks based onthe phone survey results is $26.33, for an average of $5.26 for each of these sixparks. For graphing purposes in Figure 3, the marginal WTP when it was computedover more than one park was split evenly between the number of additional parksused in the estimate; that is why these regions look flat. The six to 10 park regionof Figure 3 was calculated using the phone survey results.

Table V shows the results of computing marginal WTP for the mail and phonesurveys. The first row is the WTP for a group of four parks when 29 already exist.The second row is the WTP for the 30th park when 29 already exist. The third rowis the WTP for the 31st park when 30 already exist. The fourth row is the WTP forthe 32nd and 33rd parks when 31 already exist. The fifth row is the WTP for sixmore parks when 34 already exist. Estimated standard errors and t-statistics for themarginal WTP are also shown. For the first increments to the park system, thet-statistics are high. The values are clearly sensitive to changes in scope. However,as the value of an additional park diminishes toward zero, we lose the power todistinguish between goods of different scope. A larger sample size would berequired to decrease the standard error, which otherwise is large with respect tothe marginal value.

The standard errors in Table V are estimates assuming zero covariance betweenvalues estimated from independent samples and assuming symmetry of the errordistribution in a very small neighborhood around the point estimates. Recall that

Ž . Ž . Ž . Ž .var A y B s var A q var B if cov A, B s 0, and that the t-value for a 95%


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ROLLINS AND LYKE338

FIG. 2. Variation of WTP by scope of good: Point estimates and 95% confidence intervals.

FIG. 3. Diminishing marginal WTP per household.

TABLE VFinding Significant Sensitivity to Scope When Marginal Willingness to Pay is Diminishing

Mail Phone

Estimated t-value for Estimated t-value forMarginal standard marginal Marginal standard marginal

Description WTP9 Error WTP WTP9 error WTP

Ž .WTP9 1 ??? 4 191.57 14.72 13.01 235.18 17.17 13.70Ž .WTP9 1 105.45 7.28 14.48Ž .WTP9 2 56.40 16.17 3.49Ž .WTP9 3 ??? 4 29.72 20.66 1.44Ž .WTP9 5 ??? 10 y3.13 17.16 y0.18 26.33 23.95 1.10

Ž . Ž .Notation. WTP9 n s marginal WTP for the nth park. WTP9 n ??? k s marginal WTP for thenth]kth parks.


Ž .confidence interval c.i. is 1.96. Because the 95% c.i. were actually computed bythe Krinsky and Robb method, the standard errors were estimated as follows:

Let U s upper bound of the 95% c.i., and

WTP s point estimate.

Ž . 11Then s s U y WTP r1.96, where s is the estimated standard error of WTP.Based on the fact that different levels of information were provided for the four

parks than for the remaining six parks, one might posit an information provisioneffect instead of diminishing marginal WTP to explain why there was littledifference between WTP for four parks versus 10 parks. This possibility was testedand rejected. The information effect could potentially have arisen because thefour-park proposal respondents were given specific information sheets about each

Žof the four parks there were only four specific park proposals, the other six were‘‘generic’’ in the sense that respondents only knew that they would be representa-

.tive of natural regions that were as yet not represented in the Parks system .Therefore respondents to the 10-park proposals who had already received aone-park proposal would have only seen a specific information sheet pertaining toone out of the 10 parks. The respondents to the 10-park proposals who had alsoreceived a four-park proposal would have seen all four specific information sheets.Therefore if there were information effects, we would anticipate that the 10-parkvalues for those receiving the four park-specific information sheets would bedifferent from the 10-park values from those receiving only the one generic sheet.

In order to more fully explore this possibility, the sample that included 10-parkquestions was split in order to determine the effect of information. A subsamplethat was asked only one CVM question, which was for 10 parks, received only thetwo common pages in their information packet. Thus they received the generaldescription of the goal to preserve examples of all 39 natural regions by creating 10parks for regions still unrepresented within the National Parks system, and a mapshowing where these natural regions were located; but were not given specificinformation about the parks proposed for the Northwest Territories. The sample

Ž .split that received both the four-park and the 10-park questions versions 9 and 10received the most complete information packets, which included separate sheetsdescribing particular details and boundaries of each of the four proposed parks inthe Northwest Territories. There was no statistical evidence that including descrip-tions of specific parks influenced values for the 10-park proposal.

11 Our method of calculating standard errors for comparing marginal differences in WTP is intuitive,and easily allows us to demonstrate the points we make in this article. The method is an approximation,assuming symmetry of the error term in a small region around the point estimates. While thecalculations of t-values are approximations, they clearly illustrate that they are generally decreasing for

w xsmaller values of marginal WTP. Poe, Severance-Lossin, and Welsh 23 provide a detailed discussion ofthe problem of testing for differences between empirical distributions created by resampling techniquesin the context of CVM, and they demonstrate the method of convolutions approach to comparedistributions.

ROLLINS AND LYKE340

V. INTERNAL CONSISTENCY AND VALIDITY TESTS

The surveys and informational materials for this study were developed toŽincorporate three different survey formats the third was a discrete choice experi-

.ment, which will be reported elsewhere and to conform to a complex experimentaldesign allowing numerous tests for internal consistency and validity of estimates.Results from tests on question ordering, yea-saying, method of survey administra-tion, information effects, and contrasting individual parks are briefly discussedhere.

In the mixed-mode survey, we tested whether the WTP estimates for the 10-parkand four-park proposals were influenced by the order in which the respondent

Žvoted: the smaller-scope project first or the larger scope project first see Table.IV . Question order tests confirmed that question order did not significantly affect

WTP estimates. The mail-only WTP for the 10-park proposal was estimated withŽ .dummy variables that indicated whether the proposal was asked alone version 12

Ž .or with a one-park proposal versions 3 through 6 or with a two-park proposalŽ . Ž .versions 7 and 8 , or a four-park proposal versions 9 and 10 . Not only did thedirections of coefficients on dummy variables show no consistent pattern based onthe scope of the first question, but none of them were statistically significant.These data do not indicate a problem arises from having included an initialquestion about a good of smaller scope. There is also no evidence of a directionalbias in the estimates from asking one question as opposed to two questions.

Mail-only versions 1]8 included different combinations of specific parks in theone-park and two-park proposals. Statistical tests did not determine any differencein WTP estimates between parks in different natural regions.

This study provides a controlled comparison between elicitation by mail versusby phone. The mixed-mode WTP for the four-park proposal was $235.18, which iswithin the 95% c.i. for the WTP for four-parks estimated by the mail-only surveyŽ .Tables III and IV , indicating that the two formats provided similar results.Demographic data of the 357 mixed-mode participants conformed well to censusdata for the national population, while demographic data from respondents to themail-only survey conform less well. The mail-only respondents were typically morehighly educated with higher average and median income levels than the census andthe mixed-mode sample. That the phone instrument resulted in a more representa-tive sample than the mail-only instrument is not surprising and has been noted

w xelsewhere 17, 2 . Differences in WTP results between the instruments were notstriking.

Some researchers have suggested that WTP estimates can be biased upward ifrespondents feel compelled to answer in a way that they think may be pleasing tothe interviewer]survey researcher, but that is not indicative of their true WTP. Inorder to test for yea-saying, or overstating their WTP in order to show support forthe proposal, a random sample of 50% of the mixed-mode respondents and a splitŽ .versions 4, 6, and 10 of the mail-only respondents were asked an additionalquestion}whether they would vote for the proposal if it effectively would costtheir household nothing to do so. We had hypothesized that giving participants theopportunity to reply yes to show their support of the proposals, even if the dollaramounts that they were given to respond to were above their maximum willingness


to pay, might reduce any potential for yea-saying. Statistical tests indicated that themean WTP was not different between those who had received a zero bid option

w xand those who did not. Gunning]Trant 13 provides a thorough description ofthese results. There was no evidence of yea-saying, that is, there was no statisticaldifference in WTP between those respondents who had the zero-bid questions andthose who did not.

The same CV question used to test for yea-saying allowed us to test for theeffect of zero bids. Respondents who checked no, indicating that they would vote

Ž .no even if it cost their household nothing to create the new park s , were assumedŽ .to be willing to pay no more than zero for the creation of the new park s . Another

question had asked how supportive respondents were of the goal of the ParksSystem to include representative examples each of the 39 NRs. The correlationbetween the ‘‘zero’’ bids and those who indicated that they disagreed or stronglydisagreed with the stated goal of the Parks System was, as expected, very high.Answers to a variety of follow-up questions as to why they voted no were consistentwith a true low valuation for creation of the new parks.12 We saw no evidence toassume that any response did not reflect the views of the participant toward thegood in question, and could not justify omitting any responses from the estimationas ‘‘outliers’’ or protest bids.

VI. IMPLICATIONS

In the light of the present study, seemingly disparate results from previouslypublished scope tests can be reconciled in a single framework. Consider studies

w xwhere contingent valuation was insufficiently sensitive to scope. Boyle et al. 4found that values for preventing migratory waterfowl deaths were not sensitive toscope. The three levels of insult considered were from less than 1% of thewaterfowl population to about 2%. Perceptually this range may have all been at theupper end of the WTP curve as in our hypothetical Study II, where large samplesizes would be required to detect significant responsiveness to scope. Similarly,

w xvalues for wilderness areas in the Diamond and Hausman 10 study did not pass ascope test. In this case, the range considered was for protecting the 49th, 50th, or49th and 50th out of 57 wilderness areas. This may have also been a range such asthat in our hypothetical Study II.

w x w xMeanwhile, the Carson et al. study 7 , Loomis and Larson 18 , and others havefound that contingent valuation results are sensitive to scope. In the Carson et al.w x7 Southern California study, for example, the two goods considered were restoringfour species in 15 years versus restoring two species in 50 years. The difference inscope between these two scenarios may have fallen in the range of our hypothetical

w xStudy I. One of the strengths of the Carson et al. 7 study was its conformity withthe NOAA guidelines. We do not believe that this alone will be sufficient to assurevalues will pass a scope test. Unless a range of scope changes is considered, CVestimates are vulnerable to being replicated except with a different specification in

12 For example, some had indicated in writing that they disagreed with Canadian Park policy thatnative peoples should have ‘‘special rights’’ to hunt in National Parks while nonnatives did not, and thuscould not support creation of new parks.

ROLLINS AND LYKE342

a change in scope that is close to the upper end of the range, and reaching theopposite conclusion about the CV method’s responsiveness to changes in scope.

Many researchers have voiced concern over the issue of scope in measures ofexistence values, and some have suggested that results such as our hypothetical

wStudies I and II in the previous text may indicate theoretical inconsistencies 2, 4, 9,x10, 22 . In our study, the difference between the two largest goods was much

smaller than the difference between three smaller goods. This is consistent withdiminishing marginal existence values for the parks system. However, if a re-searcher had not known the shape of the marginal value curve, and had concen-trated on the larger scope goods, for which the successive increments were so smallas to be indistinguishable by empirical methods, it might have erroneously beenconcluded that people do not distinguish by the scope of the good. This studyindicates that people do distinguish between existence goods of different scope, butdue to diminishing marginal valuations for larger scope goods, the differencesbetween the values of larger scope goods may be negligible unless sample sizes areadjusted accordingly.

In measuring existence values using contingent valuation, it is necessary to do soin a policy-relevant framework in which the good is anchored within a context thatclearly defines the relevant range of scope: how much of the good already exists,what would remain if the policy action is not carried out, and an upper limitdescribing how much of the good is ‘‘sufficient’’ in terms of a policy-relevantcontext.

Our work makes three contributions to the debate over whether CV existenceestimates are sensitive to scope, what an adequate test for sensitivity to scope mustinvolve and theoretical reasons for why some studies do and others do not result inestimates that are sensitive to scope. The first point involves the importance of a

w xwell-defined CV good. We are not the first to make this point 11 , yet it is worthreiterating how important it is to ‘‘peg’’ the end-points of the existence good inorder to understand what the WTP curve may look like and where on the WTPcurve a good of a given scope would lie. The second point involves the interpreta-tion of scope tests. Our work indicates that it is necessary to recognize the dangerof false rejection because the scope test was carried out within a range of the WTPcurve too close to the upper end-point for the sample size to detect differences inscope. A good idea for future CV work is to use at least two ranges, as this studydid. The added expense of splitting the sample to do so is not great relative to theinitial investment in survey design and implementation. The third point involvessample sizes for scope tests. It should be recognized that the upper ends of rangeswill require larger samples, and an experimental design plan should reflect this.

APPENDIX: SAMPLE CV QUESTIONS

Double-bounded CV questions for the two proposal two-park and 10-parkversion of the mail survey are shown in the following text. In the two-proposalversions, the two proposals appeared on separate pages. Those participants whoreceived two proposals were instructed to respond to each as if it were the onlyoption that they had to consider. Copies of all survey materials are available fromthe authors upon request. See Figures A1 and A2.


PROPOSAL 1:

Parks Canada would create East Arm of Great Slave Lake National Park and North Baffin and BylotIsland National Park as described in your information booklet.

REFERENDUM QUESTION: Would you öte for or against proposal 1 under each of the conditionsŽ .below? CHECK ONE BOX EACH FOR 6a AND 6b :

VOTE VOTEAGAINST FOR

6a. If it added a one-time tax of $ I Ito your 1995 tax bill?

6b. If it added a one-time tax of $ I Ito your 1995 tax bill?

FIGURE A1

PROPOSAL 2:

A second option would be for Parks Canada to create East Arm of Great Slave Lake National Park andNorth Baffin and Bylot Island National Park plus 8 additional parks, one in each of the 8 remainingNatural Regions. A total of 10 parks would be created, and all 39 natural regions would be representedin the Parks System.

REFERENDUM QUESTION: Would you öte for or against proposal 2 under each of the conditionsŽ .below? CHECK ONE BOX EACH FOR 7a AND 7b :

VOTE VOTEAGAINST FOR

7a. If it added a one-time tax of $ I Ito your 1995 tax bill?

7b. If it added a one-time tax of $ I Ito your 1995 tax bill?

FIGURE A2

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The Case for Diminishing Marginal Existence Values1

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