This comment takes up the discussion about the incentive compatibility of contingent valuation surveys revived by a recent paper of Carson, Groves and List (2014) in this journal. We feel that the conclusions the authors draw from their theoretical and experimental work cannot be generalized to contingent valuation (CV) surveys. We single out the lack of cost credibility as the principal obstacle to incentive compatibility and propose some amendments to the survey protocol that foster the cost credibility of random-bid CV studies

Rheinberger, Christoph

Schläpfer, Felix

Name not available

 TSE‐573
	
It’s	the	Cost	Credibility,	Stupid!	A	Comment	on	
“Consequentiality:	A	Theoretical	and	Experimental	
Exploration	of	a	Single	Binary	Choice”	
	
	
Christoph	M.	Rheinberger	and	Felix	Schläpfer	
May	2015
It’s the Cost Credibility, Stupid! A Comment on
“Consequentiality: A Theoretical and Experimental
Exploration of a Single Binary Choice”
Christoph M. Rheinberger and Felix Schläpferú
May 1, 2015
Abstract
This comment takes up the discussion about the incentive compatibility of contingent
valuation surveys revived by a recent paper of Carson, Groves and List (2014) in this
journal. We feel that the conclusions the authors draw from their theoretical and
experimental work cannot be generalized to contingent valuation (CV) surveys. We
single out the lack of cost credibility as the principal obstacle to incentive compatibility
and propose some amendments to the survey protocol that foster the cost credibility of
random-bid CV studies.
JEL Codes: D81, D82, Q51.
Keywords: Contingent valuation, cost credibility, incentive compatibility.
úRheinberger: Toulouse School of Economics (LERNA), Allée de Brienne 21, 31000 Toulouse, France
(e-mail: rheinberger.cm@gmail.com); Schläpfer: Kalaidos University of Applied Sciences, Jungholzstrasse
43, 8050 Zurich, Switzerland (e-mail: felix.schlaepfer@kalaidos-fh.ch).
1
In what might be called a decennial project Carson, Groves and List (2014, hereafter CGL)
theoretically and experimentally explore the incentive properties of the single binary choice
(SBC) mechanism and prove that SBC are, under some assumptions, incentive compatible.
We endorse the elegance of CGL’s proof, but doubt that it applies to the binary referendum
with randomly assigned bids that the NOAA panel (Arrow et al. 1993) recommended as blue
print for contingent valuation (CV) surveys. In this comment we contend that the random
bid assignment makes binary referendum CV surveys incentive incompatible because, by
their very nature, random bids di er for most respondents from the actual cost of the project
under consideration.
We seize on a number of arguments that have been made before (Green et al. 1998;
Horowitz 2000; Flores and Strong 2007; Schläpfer 2008), but that have been largely ignored
by the field. Our comment is structured as follows. We first summarize the argumentation
of CGL and formally show that their proof of incentive compatibility readily applies to a
binary referendum with unambiguous actual costs. We then demonstrate that incentive
compatibility does not hold as soon as actual costs and randomly assigned bids di er. We
discuss this negative result in light of its consequences for CV practitioners and propose
amendments to the CV protocol that provide some means for relief, but no cure.
1 Binary referendum with unambiguous actual costs
In the first part of their paper, CGL provide eight propositions that pin down the conditions
under which binary referendums with unambiguous actual costs are incentive compatible.
They then present a field experiment in which subjects voted for or against the provision of
a public good in exchange for a lump sum payment equal to their show-up fee. The results
support their theoretical claim that truthful revelation of preferences is the optimal strategy
as long as choices are believed to be consequential. From this CGL conclude (2014:195) that
“consequentiality and realism need to permeate all parts of a valuation survey”. We could not
2
agree more with this conclusion. However, the mechanism of CGL’s field experiment di ers
decisively from the mechanism of random bid CV surveys. While their subjects faced a binary
referendum with known, unambiguous and non-negotiable costs, a typical CV respondent is
presented with a randomly assigned bid that might be very di erent from what they actually
had to pay if the referendum passed.
The di erence might seem subtle at first but, as already noted by Horowitz (2000), it
creates incentives for various strategic behaviors. We will draw on the behavioral model of
Green et al. (1998) to substantiate this claim.1 Consider a CV respondent i who believes the
probability of implementing a project, conditioned on actual cost c, is proportional to the
survey plurality for the project at this cost. Let r denote the largest bid at which i will still
approve the project. Similar to CGL’s field experiment we shall first presume that i’s actual
cost share is known, unambiguous and non-negotiable. The plurality for implementation of
the project at the respondent’s actual cost is given by N≠1 (n(1≠ F (c)) + 1(r Ø c)), where
N = n+1 is the number of CV respondents and F (·) is a CDF that reflects i’s beliefs about
the responses of the other n respondents. The indicator function 1(·) is equal to one if its
argument is true and zero otherwise.
If the respondent believes her vote is consequential she will choose a response that
maximizes her expected payo  E [ﬁ], which is simply the di erence between her true but
unobserved willingness-to-pay Ê˜ and her actual cost share in the project multiplied by her
subjective probability of approval:
E [ﬁ] = (Ê˜ ≠ c)⁄N≠1 (n(1≠ F (c)) + 1(r Ø c))
= K + ⁄N≠1 s r0 (Ê˜ ≠ c)GÕ(c)dc. (1)
K is a constant term independent of r, ⁄ reflects i’s belief about the consequentiality of her
response, and G(·) is the CDF of i’s belief about c conditioned on the framing of the survey.
If c is known, the payo  function is maximized at r = Ê˜ as long as GÕ(·) is positive in the
1Although the Green et al. model is rooted in expected utility, its results readily apply to CGL’s model.
3
vicinity of Ê˜. Hence, the respondent will answer truthfully if she believes that:
(i) There is one and only one project to be approved or rejected;
(ii) The survey answer is deemed consequential, i.e. ⁄ > 0;
(iii) The probability of implementation is proportional to survey plurality; and
(iv) The payment vehicle is decoupled in the sense that r has no impact on c.2
The attentive reader will note that the set of beliefs invoked by Green et al. (1998) are
consistent with both the propositions and the field experiment presented by CGL. Holding
these beliefs leads to a trivial Nash equilibrium in which i’s optimal action does not depend
on the actions of the other n respondents. In other words, a truthful answer is the best
strategy to play.
2 When bids di er from actual costs
Unfortunately, inducing the above set of beliefs in a CV survey is less trivial than many
researchers seem to presume. Perhaps the biggest concern relates to belief (iv). In CV
studies, bids are randomly assigned to respondents to generate the statistical variation that
enables the estimation of willingness-to-pay values. While statistically sound, the random
assignment makes some bids incredibly high or low for there are always poor respondents
who receive high bids and wealthy respondents who receive low bids (Flores and Strong
2007). Why does this matter? Let us reconsider the expected payo , only that this time we
replace c by the anticipated cost c˜ = „˜c, where „˜ is an unobserved scaling factor expressing
the respondent’s belief about her cost relative to the average person’s cost. For example, a
wealthy and a poor respondent may have scaling factors of „˜ = 5 and „˜ = 0.5, respectively.
Not surprisingly, the poor respondent has an incentive to overstate Ê˜ while the wealthy
2In the framework of Carson and Groves (2007:191), belief (iv) is replaced by the belief that the price
(i.e. the bid) o ered in the survey is equal to the true cost c: “The agent needs to believe that if the agency
implements a particular alternative: the specified good Q will be provided and the stated price P will be
assessed.” In substance, the two beliefs are equal. Yet Carson and Groves make it explicit that respondents
must take the bid at face value for SBC questions to be incentive compatible.
4
respondent has an incentive to understate Ê˜.3
Under which conditions should we expect CV respondents to process the bids assigned
to them and hence to answer di erent questions than those asked in the survey? One answer is
whenever belief (iv) breaks down; that is, whenever the respondent has any reason to believe
that what they state may not only a ect the probability of approval, but also the amount of
the good provided or the cost charged for its provision (Horowitz 2000). Yet, as just shown,
it is not even necessary that the respondent abandons belief (iv). It su ces that they believe
their own contribution would di er from the median person’s contribution (Flores and Strong
2007). This seems a reasonable belief in many cases of public good provisions—for instance,
when the project is to be financed through common sources of tax revenue (income taxes,
property taxes) or relative to individual consumption (water bills) or stake (shareholding in
co-property). In all of these settings respondents might actually believe their answer is going
to a ect the probability of approval but not the overall amount or cost of the public good.
They may nevertheless over- or understate their willingness-to-pay for the project, simply
because they infer the anticipated cost from the bid presented to them.
What about bids that are framed as one-time lump sum tax payments? Under this
payment mechanism, which is closest to the binary referendum format endorsed by the NOAA
panel, the respondent may behave strategically if they doubt that the payment mechanism
is coercive. Such doubts might be well justified. Take a person who lives on social security
and receives the invitation to participate in a CV study on the amelioration of a public park.
It seems obvious to us that the respondent would anticipate he could not be forced to make
a payment of, say, $200.
How big an issue is the lack of cost credibility? Empirical evidence on cost credibility
is still scarce, but the little evidence we have suggests that a considerable proportion of
respondents do not believe in the bids presented to them. In a CV study on open space
3If we were to know „˜, we could even predict the optimal over- or understatement. Consider the modified
payo  function E [ﬁ] = Kú + ⁄N≠1
s r
0 (Ê˜ ≠ „˜c)GÕ(c)dc, which is maximized at r = Ê˜/„˜. It is optimal for a
respondent with „˜ to state an amount that is exactly 1/„˜ times their true willingness-to-pay.
5
preservation in Colorado, Champ et al. (2002) found that 38% of the respondents believed
their actual contribution would be higher than the bid they faced, while 4% believed their
actual contribution would be lower. Flores and Strong (2007) report on a CV study valuing
the local clean up of mine contamination in which only one third of the respondents believed
that the presented bids would match their actual cost. Again, there were far more respondents
(63%) who thought they ought to pay more than the bid amount if the project was to be
implemented. The proportion of cost skeptics has to be judged against the relatively narrow
bid ranges used in these studies ($10-$140 and $17-$270, respectively). In agreement with
Flores and Strong (2007), we strongly suspect that the proportion of cost skeptics would be
even larger with a wider bid range.
3 Means to reduce strategic behavior
Although far from conclusive, the evidence on the lack of cost credibility in random-bid
CV studies is alarming and calls for more attention in the way researchers ask the payment
questions. Here, we summarize two ideas that have been proposed to foster the credibility of
the cost credibility of CV studies.4
Realistic costs. The first idea is to use real, or better realistic, cost estimates as bids.
For example, Johnston (2006) presents a CV study in which respondents voted on a water
supply project. The respondents received random bids from a realistic range of costs, which
experts had estimated based on data from neighboring water districts and engineering cost
estimates. This decreases the scope for overstating the true willingness-to-pay because each
respondent faced a bid that could, with some probability, be their actual cost of the project.
We emphasize that the use of realistic cost estimates does not eliminate strategic behavior
as there is still some chance that respondents deem the survey answer to be non-coercive.
4An alternative approach, which we do not pursue here, is based on recent progress in the econometrics
of choice modeling. It is conceivable that the unobserved heterogeneity in the anticipated cost c˜ can be
structurally modeled as a latent variable. The reader is referred to Walker and Ben-Akiva (2002) for a con-
ceptual discussion, and to Hess and Beharry-Borg (2012) and Lundhede et al. (2015) for recent applications
in environmental economics.
6
Moreover, the approach requires a relatively narrow cost bracket so that the cost range is
credible and, hence, it might not provide the necessary variation in responses to reliably
estimate the willingness-to-pay distribution.5
Exploiting heterogeneity in individual cost shares. As a means of addressing this prob-
lem, Strong and Flores (2008) turn to variations in federal/local cost shares, thereby creating
di erent costs to respondents while maintaining a link to the project’s estimated cost. In
many applications it is even more convincing to generate variation by making the bids con-
tingent on the respondent’s last tax invoice. This can be achieved by framing the payment
vehicle as a percentage increment in income taxes (Schläpfer 2008). In online surveys, it
su ces to inquire about the respondent’s last tax invoice and to present them with the ab-
solute bid amounts corresponding to their tax payments; in pen-and-pencil surveys, simple
conversion tables may help the respondent to convert relative increment into absolute bid
amounts.6 Income heterogeneity among the respondents then generates the variation needed
for statistical identification in a credible manner.
Of course, respondents could still game the survey by stating unrealistically low num-
bers. Yet we believe that these two features reduce the scope of strategic behavior and foster
the cost credibility of CV studies, particularly when combined with a thorough description
of the payment mechanism that is foreseen to provide the public good. As Horowitz states
(2000:69): “[I]n an open society it is important that citizens know what mechanism is being
used to make public goods decisions.”
4 Concluding remarks
CGL provide a paramount example of a SBC referendum question that is incentive compati-
ble. The sports memorabilia fans who participated in their field experiment could only decide
5In Johnston’s CV study on water supply, bids ranged from $125 to $425 per quarter. Corresponding
approval rates dropped from 65.3% to 32.6%. The high approval of the largest bid used by Johnston makes
it di cult to econometrically nail down the right tail of the willingness-to-pay distribution.
6An exemplary conversion table can be found in Schläpfer and Schmitt (2007).
7
whether to approve or reject the provision of a ticket stub to a prominent baseball game.
There was no hope whatsoever that a rejection of the proposal would result in a more at-
tractive proposal, ruling out logrolling. Participants had also no reason to believe they could
be tricked. The voting mechanism was clearly stated and nobody could over- or understate
their willingness-to-pay for receiving the stub. It is incontestable that in such situations SBC
referendum questions are incentive compatible. This does not, however, imply in that CV
studies using the random-bid SBC format are incentive compatible. To the contrary—if a
lack of cost credibility induces strategic misrepresentation, then ensuring consequentiality as
stipulated by CGL will only support strategic misrepresentation.
Some economists have concluded that CV studies are a “hopeless” enterprise to para-
phrase Hausman (2012). We do not feel that such a drastic conclusion is warranted, but
we certainly believe that cost credibility deserves more attention in the debate about the
incentive compatibility of CV studies.
8
References
Arrow, Kenneth, Robert Solow, Paul R. Portney, Edward E. Leamer, Roy Radner, and
Howard Schuman. 1993. “Report of the NOAA Panel on Contingent Valuation.” Federal
Register 58:4601–4614.
Carson, Richard T. and Theodore Groves. 2007. “Incentive and informational properties of
preference questions.” Environmental and Resource Economics 37 (1):181–210.
Carson, Richard T., Theodore Groves, and John A. List. 2014. “Consequentiality: A Theo-
retical and Experimental Exploration of a Single Binary Choice.” Journal of the Association
of Environmental and Resource Economists 1 (1):171–207.
Champ, Patricia A., Nicholas E. Flores, Thomas C. Brown, and James Chivers. 2002. “Con-
tingent valuation and incentives.” Land Economics 78 (4):591–604.
Flores, Nicholas E. and Aaron Strong. 2007. “Cost credibility and the stated preference
analysis of public goods.” Environmental and Resource Economics 29 (3):195–205.
Green, Donald P., Karen E. Jacowitz, Daniel Kahneman, and Daniel McFadden. 1998. “Ref-
erendum contingent valuation, anchoring, and willingness to pay for public goods.” Resource
and Energy Economics 20 (2):85–116.
Hausman, Jerry. 2012. “Contingent valuation: from dubious to hopeless.” Journal of Eco-
nomic Perspectives 26 (4):43–56.
Hess, Stephane and Nesha Beharry-Borg. 2012. “Accounting for Latent Attitudes in
Willingness-to-Pay Studies: The Case of Coastal Water Quality Improvements in Tobago.”
Environmental and Resource Economics 52 (1):109–131.
Horowitz, John K. 2000. “Policy discussion section of “stated preference: what do we know?
where do we go?”.” In Proceedings of “Theory and Design of Stated Preference Methods”,
A Workshop Sponsored by the USEPA’s National Center for Environmental Economics and
9
National Center for Environmental Research. October 12–13, Doubletree Hotel, Washing-
ton, D.C.: http://epa.gov/ncer/publications/workshop /pdf/EE-0436-01.pdf.
Johnston, Robert J. 2006. “Is Hypothetical Bias Universal? Validating Contingent Valuation
Responses Using a Binding Public Referendum.” Journal of Environmental Economics and
Management 52 (1):469–481.
Lundhede, Thomas, Jette Bredahl Jacobsen, Nick Hanley, Niels Strange, and Bo Jellesmark
Thorsen. 2015. “Incorporating outcome uncertainty and prior outcome beliefs in stated
preferences.” Land Economics 91 (2):296–316.
Schläpfer, Felix. 2008. “Contingent valuation: A new perspective.” Ecological Economics
64 (4):729–740.
Schläpfer, Felix and Marcel Schmitt. 2007. “Anchors, endorsements, and preferences: A field
experiment.” Resource and Energy Economics 29 (3):229–243.
Strong, Aaron and Nicholas E. Flores. 2008. “Estimating the economic benefits of the clean
up of acidic rock drainage using cost shares.” Ecological Economics 65 (2):348–355.
Walker, Joan and Moshe Ben-Akiva. 2002. “Generalized random utility model.” Mathematical
Social Sciences 43 (3):303–343.
10


It’s the Cost Credibility, Stupid! A Comment on “Consequentiality: A Theoretical and Experimental Exploration of a Single Binary Choice”

Rheinberger, Christoph M.

Toulouse Capitole Publications

 TSE‐573	It’s	the	Cost	Credibility,	Stupid!	A	Comment	on	“Consequentiality:	A	Theoretical	and	Experimental	Exploration	of	a	Single	Binary	Choice”			Christoph	M.	Rheinberger	and	Felix	Schläpfer	May	2015It’s the Cost Credibility, Stupid! A Comment on“Consequentiality: A Theoretical and ExperimentalExploration of a Single Binary Choice”Christoph M. Rheinberger and Felix SchläpferúMay 1, 2015AbstractThis comment takes up the discussion about the incentive compatibility of contingentvaluation surveys revived by a recent paper of Carson, Groves and List (2014) in thisjournal. We feel that the conclusions the authors draw from their theoretical andexperimental work cannot be generalized to contingent valuation (CV) surveys. Wesingle out the lack of cost credibility as the principal obstacle to incentive compatibilityand propose some amendments to the survey protocol that foster the cost credibility ofrandom-bid CV studies.JEL Codes: D81, D82, Q51.Keywords: Contingent valuation, cost credibility, incentive compatibility.úRheinberger: Toulouse School of Economics (LERNA), Allée de Brienne 21, 31000 Toulouse, France(e-mail: rheinberger.cm@gmail.com); Schläpfer: Kalaidos University of Applied Sciences, Jungholzstrasse43, 8050 Zurich, Switzerland (e-mail: felix.schlaepfer@kalaidos-fh.ch).1In what might be called a decennial project Carson, Groves and List (2014, hereafter CGL)theoretically and experimentally explore the incentive properties of the single binary choice(SBC) mechanism and prove that SBC are, under some assumptions, incentive compatible.We endorse the elegance of CGL’s proof, but doubt that it applies to the binary referendumwith randomly assigned bids that the NOAA panel (Arrow et al. 1993) recommended as blueprint for contingent valuation (CV) surveys. In this comment we contend that the randombid assignment makes binary referendum CV surveys incentive incompatible because, bytheir very nature, random bids di er for most respondents from the actual cost of the projectunder consideration.We seize on a number of arguments that have been made before (Green et al. 1998;Horowitz 2000; Flores and Strong 2007; Schläpfer 2008), but that have been largely ignoredby the field. Our comment is structured as follows. We first summarize the argumentationof CGL and formally show that their proof of incentive compatibility readily applies to abinary referendum with unambiguous actual costs. We then demonstrate that incentivecompatibility does not hold as soon as actual costs and randomly assigned bids di er. Wediscuss this negative result in light of its consequences for CV practitioners and proposeamendments to the CV protocol that provide some means for relief, but no cure.1 Binary referendum with unambiguous actual costsIn the first part of their paper, CGL provide eight propositions that pin down the conditionsunder which binary referendums with unambiguous actual costs are incentive compatible.They then present a field experiment in which subjects voted for or against the provision ofa public good in exchange for a lump sum payment equal to their show-up fee. The resultssupport their theoretical claim that truthful revelation of preferences is the optimal strategyas long as choices are believed to be consequential. From this CGL conclude (2014:195) that“consequentiality and realism need to permeate all parts of a valuation survey”. We could not2agree more with this conclusion. However, the mechanism of CGL’s field experiment di ersdecisively from the mechanism of random bid CV surveys. While their subjects faced a binaryreferendum with known, unambiguous and non-negotiable costs, a typical CV respondent ispresented with a randomly assigned bid that might be very di erent from what they actuallyhad to pay if the referendum passed.The di erence might seem subtle at first but, as already noted by Horowitz (2000), itcreates incentives for various strategic behaviors. We will draw on the behavioral model ofGreen et al. (1998) to substantiate this claim.1 Consider a CV respondent i who believes theprobability of implementing a project, conditioned on actual cost c, is proportional to thesurvey plurality for the project at this cost. Let r denote the largest bid at which i will stillapprove the project. Similar to CGL’s field experiment we shall first presume that i’s actualcost share is known, unambiguous and non-negotiable. The plurality for implementation ofthe project at the respondent’s actual cost is given by N≠1 (n(1≠ F (c)) + 1(r Ø c)), whereN = n+1 is the number of CV respondents and F (·) is a CDF that reflects i’s beliefs aboutthe responses of the other n respondents. The indicator function 1(·) is equal to one if itsargument is true and zero otherwise.If the respondent believes her vote is consequential she will choose a response thatmaximizes her expected payo  E [fi], which is simply the di erence between her true butunobserved willingness-to-pay Ê˜ and her actual cost share in the project multiplied by hersubjective probability of approval:E [fi] = (Ê˜ ≠ c)⁄N≠1 (n(1≠ F (c)) + 1(r Ø c))= K + ⁄N≠1 s r0 (Ê˜ ≠ c)GÕ(c)dc. (1)K is a constant term independent of r, ⁄ reflects i’s belief about the consequentiality of herresponse, and G(·) is the CDF of i’s belief about c conditioned on the framing of the survey.If c is known, the payo  function is maximized at r = Ê˜ as long as GÕ(·) is positive in the1Although the Green et al. model is rooted in expected utility, its results readily apply to CGL’s model.3vicinity of Ê˜. Hence, the respondent will answer truthfully if she believes that:(i) There is one and only one project to be approved or rejected;(ii) The survey answer is deemed consequential, i.e. ⁄ > 0;(iii) The probability of implementation is proportional to survey plurality; and(iv) The payment vehicle is decoupled in the sense that r has no impact on c.2The attentive reader will note that the set of beliefs invoked by Green et al. (1998) areconsistent with both the propositions and the field experiment presented by CGL. Holdingthese beliefs leads to a trivial Nash equilibrium in which i’s optimal action does not dependon the actions of the other n respondents. In other words, a truthful answer is the beststrategy to play.2 When bids di er from actual costsUnfortunately, inducing the above set of beliefs in a CV survey is less trivial than manyresearchers seem to presume. Perhaps the biggest concern relates to belief (iv). In CVstudies, bids are randomly assigned to respondents to generate the statistical variation thatenables the estimation of willingness-to-pay values. While statistically sound, the randomassignment makes some bids incredibly high or low for there are always poor respondentswho receive high bids and wealthy respondents who receive low bids (Flores and Strong2007). Why does this matter? Let us reconsider the expected payo , only that this time wereplace c by the anticipated cost c˜ = „˜c, where „˜ is an unobserved scaling factor expressingthe respondent’s belief about her cost relative to the average person’s cost. For example, awealthy and a poor respondent may have scaling factors of „˜ = 5 and „˜ = 0.5, respectively.Not surprisingly, the poor respondent has an incentive to overstate Ê˜ while the wealthy2In the framework of Carson and Groves (2007:191), belief (iv) is replaced by the belief that the price(i.e. the bid) o ered in the survey is equal to the true cost c: “The agent needs to believe that if the agencyimplements a particular alternative: the specified good Q will be provided and the stated price P will beassessed.” In substance, the two beliefs are equal. Yet Carson and Groves make it explicit that respondentsmust take the bid at face value for SBC questions to be incentive compatible.4respondent has an incentive to understate Ê˜.3Under which conditions should we expect CV respondents to process the bids assignedto them and hence to answer di erent questions than those asked in the survey? One answer iswhenever belief (iv) breaks down; that is, whenever the respondent has any reason to believethat what they state may not only a ect the probability of approval, but also the amount ofthe good provided or the cost charged for its provision (Horowitz 2000). Yet, as just shown,it is not even necessary that the respondent abandons belief (iv). It su ces that they believetheir own contribution would di er from the median person’s contribution (Flores and Strong2007). This seems a reasonable belief in many cases of public good provisions—for instance,when the project is to be financed through common sources of tax revenue (income taxes,property taxes) or relative to individual consumption (water bills) or stake (shareholding inco-property). In all of these settings respondents might actually believe their answer is goingto a ect the probability of approval but not the overall amount or cost of the public good.They may nevertheless over- or understate their willingness-to-pay for the project, simplybecause they infer the anticipated cost from the bid presented to them.What about bids that are framed as one-time lump sum tax payments? Under thispayment mechanism, which is closest to the binary referendum format endorsed by the NOAApanel, the respondent may behave strategically if they doubt that the payment mechanismis coercive. Such doubts might be well justified. Take a person who lives on social securityand receives the invitation to participate in a CV study on the amelioration of a public park.It seems obvious to us that the respondent would anticipate he could not be forced to makea payment of, say, $200.How big an issue is the lack of cost credibility? Empirical evidence on cost credibilityis still scarce, but the little evidence we have suggests that a considerable proportion ofrespondents do not believe in the bids presented to them. In a CV study on open space3If we were to know „˜, we could even predict the optimal over- or understatement. Consider the modifiedpayo  function E [fi] = Kú + ⁄N≠1s r0 (Ê˜ ≠ „˜c)GÕ(c)dc, which is maximized at r = Ê˜/„˜. It is optimal for arespondent with „˜ to state an amount that is exactly 1/„˜ times their true willingness-to-pay.5preservation in Colorado, Champ et al. (2002) found that 38% of the respondents believedtheir actual contribution would be higher than the bid they faced, while 4% believed theiractual contribution would be lower. Flores and Strong (2007) report on a CV study valuingthe local clean up of mine contamination in which only one third of the respondents believedthat the presented bids would match their actual cost. Again, there were far more respondents(63%) who thought they ought to pay more than the bid amount if the project was to beimplemented. The proportion of cost skeptics has to be judged against the relatively narrowbid ranges used in these studies ($10-$140 and $17-$270, respectively). In agreement withFlores and Strong (2007), we strongly suspect that the proportion of cost skeptics would beeven larger with a wider bid range.3 Means to reduce strategic behaviorAlthough far from conclusive, the evidence on the lack of cost credibility in random-bidCV studies is alarming and calls for more attention in the way researchers ask the paymentquestions. Here, we summarize two ideas that have been proposed to foster the credibility ofthe cost credibility of CV studies.4Realistic costs. The first idea is to use real, or better realistic, cost estimates as bids.For example, Johnston (2006) presents a CV study in which respondents voted on a watersupply project. The respondents received random bids from a realistic range of costs, whichexperts had estimated based on data from neighboring water districts and engineering costestimates. This decreases the scope for overstating the true willingness-to-pay because eachrespondent faced a bid that could, with some probability, be their actual cost of the project.We emphasize that the use of realistic cost estimates does not eliminate strategic behavioras there is still some chance that respondents deem the survey answer to be non-coercive.4An alternative approach, which we do not pursue here, is based on recent progress in the econometricsof choice modeling. It is conceivable that the unobserved heterogeneity in the anticipated cost c˜ can bestructurally modeled as a latent variable. The reader is referred to Walker and Ben-Akiva (2002) for a con-ceptual discussion, and to Hess and Beharry-Borg (2012) and Lundhede et al. (2015) for recent applicationsin environmental economics.6Moreover, the approach requires a relatively narrow cost bracket so that the cost range iscredible and, hence, it might not provide the necessary variation in responses to reliablyestimate the willingness-to-pay distribution.5Exploiting heterogeneity in individual cost shares. As a means of addressing this prob-lem, Strong and Flores (2008) turn to variations in federal/local cost shares, thereby creatingdi erent costs to respondents while maintaining a link to the project’s estimated cost. Inmany applications it is even more convincing to generate variation by making the bids con-tingent on the respondent’s last tax invoice. This can be achieved by framing the paymentvehicle as a percentage increment in income taxes (Schläpfer 2008). In online surveys, itsu ces to inquire about the respondent’s last tax invoice and to present them with the ab-solute bid amounts corresponding to their tax payments; in pen-and-pencil surveys, simpleconversion tables may help the respondent to convert relative increment into absolute bidamounts.6 Income heterogeneity among the respondents then generates the variation neededfor statistical identification in a credible manner.Of course, respondents could still game the survey by stating unrealistically low num-bers. Yet we believe that these two features reduce the scope of strategic behavior and fosterthe cost credibility of CV studies, particularly when combined with a thorough descriptionof the payment mechanism that is foreseen to provide the public good. As Horowitz states(2000:69): “[I]n an open society it is important that citizens know what mechanism is beingused to make public goods decisions.”4 Concluding remarksCGL provide a paramount example of a SBC referendum question that is incentive compati-ble. The sports memorabilia fans who participated in their field experiment could only decide5In Johnston’s CV study on water supply, bids ranged from $125 to $425 per quarter. Correspondingapproval rates dropped from 65.3% to 32.6%. The high approval of the largest bid used by Johnston makesit di cult to econometrically nail down the right tail of the willingness-to-pay distribution.6An exemplary conversion table can be found in Schläpfer and Schmitt (2007).7whether to approve or reject the provision of a ticket stub to a prominent baseball game.There was no hope whatsoever that a rejection of the proposal would result in a more at-tractive proposal, ruling out logrolling. Participants had also no reason to believe they couldbe tricked. The voting mechanism was clearly stated and nobody could over- or understatetheir willingness-to-pay for receiving the stub. It is incontestable that in such situations SBCreferendum questions are incentive compatible. This does not, however, imply in that CVstudies using the random-bid SBC format are incentive compatible. To the contrary—if alack of cost credibility induces strategic misrepresentation, then ensuring consequentiality asstipulated by CGL will only support strategic misrepresentation.Some economists have concluded that CV studies are a “hopeless” enterprise to para-phrase Hausman (2012). We do not feel that such a drastic conclusion is warranted, butwe certainly believe that cost credibility deserves more attention in the debate about theincentive compatibility of CV studies.8ReferencesArrow, Kenneth, Robert Solow, Paul R. Portney, Edward E. Leamer, Roy Radner, andHoward Schuman. 1993. “Report of the NOAA Panel on Contingent Valuation.” FederalRegister 58:4601–4614.Carson, Richard T. and Theodore Groves. 2007. “Incentive and informational properties ofpreference questions.” Environmental and Resource Economics 37 (1):181–210.Carson, Richard T., Theodore Groves, and John A. List. 2014. “Consequentiality: A Theo-retical and Experimental Exploration of a Single Binary Choice.” Journal of the Associationof Environmental and Resource Economists 1 (1):171–207.Champ, Patricia A., Nicholas E. Flores, Thomas C. Brown, and James Chivers. 2002. “Con-tingent valuation and incentives.” Land Economics 78 (4):591–604.Flores, Nicholas E. and Aaron Strong. 2007. “Cost credibility and the stated preferenceanalysis of public goods.” Environmental and Resource Economics 29 (3):195–205.Green, Donald P., Karen E. Jacowitz, Daniel Kahneman, and Daniel McFadden. 1998. “Ref-erendum contingent valuation, anchoring, and willingness to pay for public goods.” Resourceand Energy Economics 20 (2):85–116.Hausman, Jerry. 2012. “Contingent valuation: from dubious to hopeless.” Journal of Eco-nomic Perspectives 26 (4):43–56.Hess, Stephane and Nesha Beharry-Borg. 2012. “Accounting for Latent Attitudes inWillingness-to-Pay Studies: The Case of Coastal Water Quality Improvements in Tobago.”Environmental and Resource Economics 52 (1):109–131.Horowitz, John K. 2000. “Policy discussion section of “stated preference: what do we know?where do we go?”.” In Proceedings of “Theory and Design of Stated Preference Methods”,A Workshop Sponsored by the USEPA’s National Center for Environmental Economics and9National Center for Environmental Research. October 12–13, Doubletree Hotel, Washing-ton, D.C.: http://epa.gov/ncer/publications/workshop /pdf/EE-0436-01.pdf.Johnston, Robert J. 2006. “Is Hypothetical Bias Universal? Validating Contingent ValuationResponses Using a Binding Public Referendum.” Journal of Environmental Economics andManagement 52 (1):469–481.Lundhede, Thomas, Jette Bredahl Jacobsen, Nick Hanley, Niels Strange, and Bo JellesmarkThorsen. 2015. “Incorporating outcome uncertainty and prior outcome beliefs in statedpreferences.” Land Economics 91 (2):296–316.Schläpfer, Felix. 2008. “Contingent valuation: A new perspective.” Ecological Economics64 (4):729–740.Schläpfer, Felix and Marcel Schmitt. 2007. “Anchors, endorsements, and preferences: A fieldexperiment.” Resource and Energy Economics 29 (3):229–243.Strong, Aaron and Nicholas E. Flores. 2008. “Estimating the economic benefits of the cleanup of acidic rock drainage using cost shares.” Ecological Economics 65 (2):348–355.Walker, Joan and Moshe Ben-Akiva. 2002. “Generalized random utility model.” MathematicalSocial Sciences 43 (3):303–343.10

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It’s the Cost Credibility, Stupid! A Comment on “Consequentiality: A Theoretical and Experimental Exploration of a Single Binary Choice”

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