Conjoint analysis is one of the most popular marketing research
tools, used in hundreds if not thousands of academic and business
research studies, e.g., see Green, Krieger, and Wind (2001) or Green and
Srinivasan (1990) for reviews. Conjoint analysis typically involves
people rating, ranking, or choosing among various options that differ by
several attributes so as to elicit consumer preferences, estimate
demand, and/or forecast market share. Until very recently, virtually all
conjoint applications were hypothetical. That is, a person's
ranking, rating, or choice had no immediate financial consequence. At
worst, hypothetical valuation questions are open to strategic
manipulation on the part of the participant, and at the least they do
not provide incentives for people to put cognitive effort into their
decisions. Over the past twenty years, a wealth of evidence has
accumulated indicating that responses to hypothetical willingness to pay
and purchase intention questions are not always consistent with
decisions when real money is on the line. For example, see the Meta
analyses in List and Gallet (2001) and Murphy et al. (2005).
Such findings have led researchers to investigate methods for
making traditional conjoint methods incentive compatible (IC). (1) One
solution, proposed by Alfnes et al. (2006), Carlsson and Martinsson
(2001), Ding, Grewal, and Liechty (2005), and Lusk and Schroeder (2004)
is to make use of traditional choice-based conjoint analysis methods,
but to randomly select one of several repeated choices between competing
product profiles as binding. The participant purchases the product
indicated as most preferred in the randomly selected choice set.
Although this approach represents a useful step forward, it is limited
to choice-based applications. Choice-based conjoint analysis has many
advantageous properties, but it is lacking on at least one front: it is
informationally inefficient relative to ranking-based conjoint
applications. In a choice-based conjoint application, all that is known
is which one option is most preferred out of a set of options. By
contrast, ranking-based conjoint applications provide information on the
consumer's complete preference ordering. These facts coupled with
the observation that ranking-based conjoint applications remain
widespread, e.g., see Baker and Burnham (2001) or Sayadi, Roa, and
Requena (2005) for recent examples, suggest it is prudent to identify
methods for making ranking-based conjoint methods IC.
The objectives of this study are: (1) to introduce a mechanism for
making conjoint rankings IC and (2) to empirically compare traditional,
hypothetical conjoint ranking responses to those using the new IC
conjoint mechanism. The new mechanism entails people ranking profiles as
in traditional conjoint analysis. However, unlike traditional conjoint
analysis, an individual actually purchases a product profile with a
probability proportional to its assigned rank. We illustrate a simple
and straightforward method to implement the IC conjoint ranking
mechanism in an empirical application related to consumer preferences
for beef attributes.
An Incentive Compatible Conjoint Ranking Mechanism
Consider a mechanism where individual i is asked to rank J products
that differ in terms of a vector of attributes [X.sub.j]. The utility
individual i derives from product j is
(1) [V.sub.ij] = [[beta].sub.i] [X.sub.j] - [[gamma].sub.i]
[P.sub.j]
where [[beta].sub.i] is a vector of marginal utilities, [P.sub.j]
is the price of alternative j, and [[gamma].sub.i] is the marginal
utility of income. Index the products such that [V.sub.i1] >
[V.sub.i2] > ... > [V.sub.i(J-1)] > [V.sub.iJ]. That is,
product j = 1 is the most preferred product, j = 2 is the next most
preferred product, and so on. The goal is to create a mechanism in which
an individual has an economic incentive to truthfully reveal their
preference ranking for the J goods. Stated differently, a mechanism is
needed wherein an individual's expected utility is maximized when
the products are ranked such that product j = 1 receives a rank of 1,
product j = 2 receives a rank of 2, and so on.
Let [r.sub.j] represent the ranking of product j such that
[r.sub.1] is the ranking of product 1, [r.sub.2] is the ranking of
product 2, and so on. An IC mechanism can be constructed by requesting
individuals to rank the J products where there is a J + 1 -
[r.sub.j]/[[summation].sup.J.sub.j=1] x 100% chance of actually
receiving product j and paying [P.sub.j]. The formula implies there is a
higher chance that an individual receives a product with a lower rank
than a product with a higher rank. For example, if there were five
products to be considered, the mechanism would ensure that there would
be a ((5 + 1 - 1)/15) x 100 = 33.3% chance of an individual actually
receiving the product ranked first, a ((5 + 1 - 2)/15) x 100 = 26.7%
chance the product ranked second would be received, and so on. The
equation stated above also ensures that there is a 100% chance that one
of the products will actually be purchased (although as will be shown in
the empirical application, one of the ranked options can be a
no-purchase option). (2)
An individual's expected utility from ranking J products is:
(2) E[U.sub.i] = [J.summation over (j=1)](J + 1 -
[r.sub.j]/[[summation over].sup.J.sub.j=1] j) [V.sub.ij].
Equation (2) shows that the expected utility derived from ranking J
goods is the sum of the probability of receiving product j times the
utility received from purchasing product j. An individual's goal is
to rank the products in a way so as to maximize expected utility given
in equation (2). It should be clear that expected utility is maximized
when an individual assigns the highest rank to product j = 1, the second
highest rank to product j = 2, and so on. This result arises because
product I was previously defined as the most preferred product, product
2 as the second most preferred product, and so on. Expected utility
cannot be made higher by assigning a more preferred product a higher
rank. This implies that the mechanism is IC; an individual's best
strategy in terms of maximizing expected utility is to assign the most
preferred product the lowest rank, the second most preferred product the
second lowest rank, and so on. The mechanism is also IC under a variety
of other nonexpected utility models. For example, under prospect theor.y
(Kahneman and Tversky 1979), individuals mis-perceive probabilities such
that probabilities, p, are weighted, w(p), in such a way that low
probabilities are over-weighted and high probabilities events are
under-weighted. However, so long as [partial derivative]w(p)/[partial
derivative]p > 0, as is assumed in prospect theory, equation (2) is
maximized by ranking the most preferred product first, the second most
preferred product second, and so on.
Although this mechanism might, at first, seem a bit complicated to
utilize in an empirical setting, it is actually quite easy to implement.
In what follows, we briefly describe one such way the mechanism can be
implemented. In many conjoint ranking applications, individuals are
given a set of cards describing each product and are requested to sort
them in terms of their preference ranking. One easy way to make such a
task IC is to create a spinning wheel of the sort found in board games
or seen on the Wheel of Fortune, where the wheel is divided into a
number of "slices" that differ in size. To facilitate decision
making, the slices can be ordered such that the largest slice appears
adjacent to the second largest slice, which appears adjacent to the
third largest slice, etc. Instead of simply requesting that individuals
hypothetical sort the cards, as is typically done, the following steps
can be taken: (1) the individual places each card on a slice on the
wheel, where the number of slices exactly equals the number of cards;
(2) after all cards are allocated, the wheel is spun; and (3) the
individual purchases the product indicated by the fixed-pointer around
which the wheel is spun. Of course, any number of other implementation
methods could be used that would ensure a profile with a lower rank has
a higher probability of being purchased. (3)
Empirical Application
In what follows, we describe an empirical application of the IC
conjoint ranking mechanism and test whether results from such a
mechanism are similar to results from traditional, hypothetical conjoint
rankings. We also explore whether making the conjoint task IC interacts
with two other treatment variables: information and product type.
Subjects
Participants were recruited near the meat counter in a suburban
grocery store located in the southeastern United States Harrison and
List (2004) discuss the advantages of carrying out value elicitation in
a field setting such as a grocery store. Subjects were offered the
chance to enter a drawing for $500 in free groceries in exchange for
participation in the study and, as will be described in more detail,
some subjects were offered free cuts of meat for participation. A total
of 515 subjects took part in the study.
Procedures
Participants were requested to rank the relative desirability of
several meat products that differed by the attributes of: (a) whether
the animal was pasture-grazed, (b) whether the animal was administered
growth hormones and antibiotics, (c) whether the meat was traceable back
to the farm, (d) package size, and (e) price. These attributes are of
interest for a number of reasons. On the policy front, there is ongoing
action related to traceability and there have been recent legislative
action to ban the use of some antibiotics in livestock production.
Valuation estimates are needed to determine the welfare effects of such
policies. On the marketing front, firms are increasingly interested in
selling "natural" products without hormones and there is
increasing interest in the value of "grass fed" beef. Although
several previous studies have estimated consumers' values for these
characteristics, e.g., Alfnes and Rickertsen (2003), Dickinson and
Bailey (2002), Lusk, Fox, and Roosen (2003), Lusk, Feldkamp, and
Schroeder (2004), Lusk, Norwood, and Pruitt (2006), McCluskey et al.
(2005), Umberger et al. (2002), to our knowledge this is the first study
to investigate preferences for pasture-raised beef relative to
nonpasture-raised beef (based on perceptions and not on taste) and to
study the effect of information about the healthfulness of such
products. This latter issue has become increasingly important as
evidenced by the USDA's recent solicitation of comments on a
proposed standard for grass-fed and pasture-fed beef claims.
The IC conjoint task involves the exchange of real money and real
food. There is some debate in the literature about the proper way to
compensate people for participating in experiments so that elicited
valuations are not unduly influenced by the compensation approach. A
common approach is to give people money for participating and then
request that participants purchase a product with the endowed money.
However, several studies have shown that people's
willingness-to-pay for a good in an experiment is significantly
influenced by the amount of money given to them (e.g., Loureiro,
Umberger, and Hine 2003; Rutstrom 1998). This led Loureiro, Umberger,
and Hine (2003) to remark (p. 271), "[n]ew ways of compensating
participants in experimental auctions should be investigated." A
solution to this problem might be to provide participants no
compensation at all. However, such an approach is likely to drastically
reduce participation rates, which would increase sample selection bias
and would significantly underestimate people's values for goods as
there are often many cash constrained people in a store setting, e.g.,
many consumers come to a store planning to pay by credit card or check
and do not have any cash to participate in a value elicitation
experiment even though they might have a positive willingness-to-pay for
the good in question.
Accordingly, we utilized a slightly different approach to
compensate participants and to estimate the marginal utility of income.
In particular, rather than asking people to pay a price for a particular
meat option, people were offered various cash amounts with each option.
In regard to this procedural choice, it is important to note three
important facts. First, one might argue that loss-aversion would create
a difference between the approach used here and one in which individuals
ranked products that they wished to purchase. However, Novemsky and
Kahneman (2005) argue that in money transactions, of the sort involved
in this exchange, there should be no loss aversion. Second, empirical
findings suggest this sort of compensation mechanism yields accurate
predictions of people's shopping behavior. For example, Lusk,
Pruitt, and Norwood (2006) found responses from an in-store experiment
where people chose between various products coupled with cash offers (as
in this study) accurately predicted actual retail sales in the grocery
store several weeks later. Further, Ding (2007) utilized a related
compensation mechanism where auction winners were paid an amount equal
to the difference in price and a certain cash amount ($250 in one
experiment and $320 in another). Ding (2007) found significantly better
out-of-sample predictive performance with this compensation mechanism as
compared to traditional hypothetical approaches where no compensation is
given at all. Finally, the purpose of this study is to compare
traditional, hypothetical conjoint response to a new IC conjoint
mechanism. In both treatments (hypothetical and nonhypothetical) people
ranked the products and cash offers in terms of which they would like to
receive. Thus our approach permits an unconfounded test of the effect of
moving from a traditional, hypothetical conjoint method to the new IC
conjoint mechanism.
Table 1 lists the attributes and attribute levels investigated in
this study. An orthogonal fractional factorial design consisting of 16
product profiles was created such that all main and two-way interaction
effects were independently identifiable. These 16 profiles were blocked
into sets of eight. Each subject was asked to rank the desirability of
the eight profiles in addition to a "no meat" option that
consisted simply of an offer of an amount of cash that was higher than
any of the cash offers that included a meat offering. This latter option
was included to account for people that participated in the study but
did not want to take home any meat. If a "cash only" offer
were not presented, it is likely that the price/cash effect would be
overstated in the sense that nonmeat preferring individuals would simply
choose meat profiles with higher cash offers. Our econometric model,
which is explained momentarily, explicitly controls for the "no
meat" option, providing an estimate of the disutility of "no
meat" holding constant price/cash. (4) Individuals were given nine
cards (eight containing a meat product description and one "no
meat" option) and were asked to rank the cards according to their
desirability.
Individuals were randomly assigned to one of the eight treatments
(there are three treatment variables each varied at two levels each,
[2.sup.3] = 8). Treatments varied according to whether: (1) the conjoint
ranking was IC or whether the ranking was hypothetical, (2) the conjoint
task related to beef steaks (ribeyes) or ground beef, and (3) whether
information was provided about the health benefits of pasture grazed
beef. The purpose for including two other treatment variables in
addition to whether the conjoint ranking was real or hypothetical was to
determine whether the IC property has an effect, not just on product
attributes, but on the effect of other treatment variables. The study
took place over a one-week time period and the treatment was alternated
every hour. The fewest number of participants in any one treatment was
59 (the hypothetical, steak, no-info treatment) and the most
participants in a treatment was 75 (the hypothetical, ground beef,
no-info treatment).
The first treatment variable is the nature of the decision task:
either hypothetical or nonhypothetical. Traditional conjoint analysis
involves people hypothetically ranking a series of product descriptions
according to their relative desirability. This is exactly what was done
in our treatments where the conjoint task was hypothetical.
Specifically, individuals in the hypothetical treatment were given the
following instructions:
For participating in this survey, we would like you to consider the
desirability of several hypothetical gifts. Although you will not
actually be given any of these gifts, we ask that you please think
carefully about your answers.
You will be viewing a poster with 9 gift coupons, each of which
describes a hypothetical gift. Gifts vary in the type and amount of
meat that you can receive. Each gift option also indicates whether
the meat comes from cattle that were raised in a pasture, were
produced without antibiotics or added growth hormones, and/or
whether the meat is traceable back to the farm. All gift options
also vary by a cash amount that would be given to you in addition
to the meat.
Your task is to sort the 9 gift coupons you have been shown in
terms of their desirability to you.
Please write the letter of the gift option you find most desirable
in the space below next to the number 1, the letter of the gift
option you find second most desirable next to the number 2, and so
on. The option you find least desirable should be put next to the
ranking of 9.
Although it is typically assumed that individuals "do their
best" and rank products according to their preferences, there is no
monetary cost to individuals deviating from their true preferences or
monetary reward for putting cognitive effort into the ranking task.
In the IC, nonhypothetical treatments, individuals were also given
nine cards to rank, but in this case, they were asked to place the cards
on a wheel that was divided into nine slices of varying size.
Participants were asked to place the option they found most desirable in
the largest slice on the wheel marked with a number one, the second most
desirable option in the second largest slot marked two, and so on. Once
all nine cards were allocated, the wheel was spun around a fixed
pointer. Once the wheel stopped spinning, the pointer indicated the
option that was actually received. Thus, in the nonhypothetical
treatments, individuals were actually given the meat and/or the cash
associated with the option that was selected by the wheel. More
specifically, participants in this treatment were instructed as follows:
For participating in this survey, we would like to offer you a
gift. You will be given 9 cards, each of which describes a gift you
might receive. Gifts vary in the type and amount of meat that you
can receive. Each gift option also indicates whether the meat comes
from cattle that were raised in a pasture, were produced without
antibiotics or added growth hormones, and/or whether the meat is
traceable back to the farm. All gift options also vary by a cash
amount that will be given to you in addition to the meat.
Your task is to sort the nine cards you have been given in terms of
their desirability to you. You should see a wheel in front of you.
You should place the gift option you find most desirable next to
the largest slot marked 1, the second most desirable gift option
you next to the second largest slot marked 2, and so on. Put the
card describing the gift option you want the least next to the
number 9 on the wheel.
Once all 9 cards are set up next to the wheel, you will spin the
wheel. Where the pointer stops will indicate the gift option you
will actually receive. This is a real decision making exercise, we
will really give you the steak and/or the cash associated with the
gift option that is selected.
The second treatment variable is product type. Because
individuals' cognitive processes may differ depending on the type
of good and whether the product is of high or low quality, we utilized
two types of meat: ground beef and ribeye steak. These two products
represent the two ends of the spectrum in terms of beef product prices
and quality; ground beef is one of the lowest price beef products,
whereas ribeye steak is one of the highest price beef products.
The final treatment variable is information. In some treatments,
participants were not given any information about the product
attributes; a situation that reflects what would happen were a consumer
to encounter a new product or brand in the marketplace where they would
have to make a purchase decision based on whatever information they had
at the time. However, firms might be interested in advertising or
providing information on the benefits of certain attributes. To
investigate this effect, some people were given the following
information:
Some gift options indicate that the meat is from Cattle Grazed in
Pasture Only. Research has shown that cattle fed a diet of grass
from pastures have higher levels of Omega 3 fatty acid, Conjugated
Linoleic Acid, and Vitamin E than grain fed beef. Research has also
shown that human consumption of Omega 3 fatty acid, Conjugated
Linoleic Acid, and Vitamin E is associated with reduced risk of
heart disease, reduced body weight, and other health benefits that
result from consumption of antioxidants.
Econometric Model
Let the deterministic portion of the utility function for person i,
alternative j, and meat type m (m = ground beef or steak) corresponding
to the conceptual model in equation (1) be rewritten as:
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where Pasture takes the value of 1 if meat option j was from cattle
that were pasture fed only and 0 otherwise, Hormone takes the value of 1
for meat products from cattle that were not administered growth hormones
or antibiotics, Trace takes the value of 1 for meat products that are
traceable back to the farm and 0 otherwise, Size takes the value of 1
for package sizes of two pounds and 0 otherwise, Cash is the amount of
money offered to the individual with option j, None takes the value of 1
for the option where no meat product was offered and 0 for all other
options, Non-Hyp equals 1 for the IC, nonhypothetical ranking treatment
and 0 for hypothetical rankings, and Info equals 1 for treatments that
provided information about pasture fed beef and 0 otherwise. The
parameters in (3) are specified to vary by meat type, m, because the
value of product attributes and the effect of the IC mechanism may
differ by meat type. Finally, let the random utility function be
specified as [U.sub.ijm] = [V.sub.ijm] + [[epsilon].sub.ijm], where
[[epsilon].sub.ijm] is an iid random error term included to indicate the
fact that people's preferences cannot be ascertained with
certainty.
Because of the ordinal nature of the dependent variable (the
person's ranking), we estimated a rank-ordered logit model that
assumes people choose the option they find most desirable and rank it
first, then choose the option they find second most desirable out of the
remaining options and rank it second, and so on. Assuming
[[epsilon].sub.ijm] are distributed type I extreme value, Beggs,
Cardell, and Hausman (1981) show that out of a set of J products, the
probability that option 1 is preferred to option 2, option 2 is
preferred to option 3, option 3 is preferred to option 4, and so on is
given by
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
which is simply the product of J - 1 multinomial logit models. In
equation (4), [[lambda].sub.ijm] is a scale parameter that is inversely
related to the variance of the error term. Typically [[lambda].sub.ijm]
is unidentifiable and is assumed equal to one. However, the relative
scale associated with different data sets or experimental treatments can
be estimated.
Estimating the relative scale parameter is important in this
application for three reasons. First, in a discrete choice model such as
this, preference/utility parameters are confounded with the scale (see
Swait and Louviere 1993). Thus, to identify the effect of moving from IC
to non-IC rankings, the relative variance of the treatments must be
controlled prior to comparing utility parameters. Second, Haab, Huang,
and Whitehead (1999) illustrated that responses to nonhypothetical
choice tasks are often less "noisy" than responses to
hypothetical choice tasks. They argue that with nonhypothetical
decisions, there are higher opportunity costs to deviating from the
rational response, which should result in a lower error variance for
nonhypothetical responses as compared to hypothetical responses. Third,
previous research has identified that error variance is increasing in
ranks (Ben-Akiva, Morikawa, and Shiroishi 1992; Hausman and Ruud 1987).
That is, there is less often "noise" in the initial ranks than
there is in the later ranks. To accommodate these issues, the scale
function is parameterized as follows:
(5) [[lambda].sub.ijm] = exp ([J-1.summation over (k=2)]
[[mu].sub.km][[rank].sub.k] + [[rho].sub.1m]Non-Hyp +
[[rho].sub.2m]Info)
where [rank.sub.k] takes the value of 1 for the kth rank ordered
choice and 0 otherwise and where [[mu].sub.k] and [[rho].sub.k] are
parameters to be estimated. Noting that exp(0) = 1, the scale function
in equation (5) takes the value of one for those data associated with
the most preferred, first rank (in which [[mu].sub.1] is implicitly set
to 0) in the hypothetical, no information treatments. Recognizing that
the scale function is inversely proportional to the error variance, we
would expect, based on the aforementioned literature, for [[mu].sub.k]
to fall as k increases and for [[rho].sub.1m] > 0. (5)
The parameters of the model are estimated by maximizing the natural
logarithm of equation (4) summed across the N individuals in the sample.
Given this model setup, the effect of moving from IC to non-IC treatment
can have a complex effect on behavior. Making the ranking task IC might
(a) increase or decrease the marginal utility of any of the product
attributes, (b) exacerbate or dampen the effect of information, and/or
(c) affect the model variance.
Results
Model estimates for ground beef and steak are presented in table 2.
The first six rows of results correspond to the estimated preferences
when treatment variables are zero, i.e., the treatment is hypothetical
and no information is presented. Results are generally consistent with a
priori expectations. Results indicate that individuals, on average,
preferred pasture-grazed beef over beef that did not have such an
attribute, beef from cattle that were not administered growth hormones
or antibiotics over hormone and antibiotic treated cattle, beef that was
traceable back to the farm versus nontraceable beef, two instead of one
pound of beef (except for steak), more cash to less, and having a pound
of beef to no beef at all.
Before moving forward, it is useful to compare these baseline
empirical results relating to people's preferences for beef product
attributes to that found in previous studies. The relative size of the
coefficients suggests participants valued the hormone attribute more
than the pasture or traceability attributes in the hypothetical
no-information treatment. This qualitative result is consistent with the
findings of Dickinson and Bailey (2002). Dickinson and Bailey (2002)
further found, using experimental auctions, that average
willingness-to-pay for traceability in roast beef sandwiches was $0.23.
In our application, willingness-to-pay for a product attribute is
calculated by taking the ratio of the attribute coefficient to the cash
coefficient. Carrying out such a calculation reveals an average
willingness-to-pay for traceability of about $1.40 per choice occasion
for ground beef and $3.19 per choice occasion for steak in the base-line
treatments. Thus, the values of traceability found here among consumers
in the southeastern United States using a conjoint ranking mechanism are
quite a bit higher than those found by Dickinson and Bailey (2002) among
people working at Utah State University using experimental auctions.
Estimates in table 2 further reveal willingness-to-pay values for
no-hormone use in the base-line treatment of $1.78 for ground beef and
$3.34 for steak. These statistics are much lower than those found by
Lusk, Roosen, and Fox (2003) who estimated the value of nonhormone use
in beef steaks at $8.12/lb for U.S. consumers using a hypothetical
choice experiment. However, the values are similar to those obtained by
Lusk and Schroeder (2004) who found that people in a choice experiment
were willing to pay between $1.36 and $3.75 (depending on the estimated
model and whether the decision task was real or hypothetical) to have a
"natural" steak rather than a "generic steak."
The next several rows of results relate to the primary hypotheses
of interest: whether behavior in the new IC ranking mechanism differed
from that in the traditional hypothetical ranking approach. For ground
beef, moving from hypothetical to IC rankings had no significant impact
on any of the utility coefficients or on the error variance.
Interestingly, preferences for ground beef were also unaffected by
information about pasture grazed beef. The lack of sensitivity to
changes in both the information and elicitation mechanism could be a
reflection of the fact that people often do not appear to behave
rationally when dealing with low-valued goods. For example, List and
Lucking-Reiley (2002) found people's behavior in auctions appeared
significantly more rational when bidding on expensive sports cards as
compared to sports cards that retailed for only $2. They argue such
behavior arises because the opportunity costs of irrational behavior
increases with the value of the good. As such, we would expect people to
be more sensitive to treatment effects when ranking higher-valued
steaks. As shown in table 2, this is exactly what we find.
In the steak model, moving from hypothetical to nonhypothetical
rankings has a number of effects. In the no information treatments,
moving from non-IC to the IC mechanism decreases the marginal utility of
pasture-raised beef, decreases "price sensitivity," and
increases the utility of "no meat." It is telling that the two
parameters, Cash and None, were significantly affected by the
hypothetical nature of the mechanism because it is these two parameters
that people would attempt to manipulate if they desired to strategically
respond to the survey. For example, Wertenbroch and Skiera (2002) argue,
(p. 230), "[i]f subjects believe that their responses will be used
to set long-term market prices, they have an incentive to under-state
their [willingness-to-pay]. If they believe that their responses will
determine the introduction of a desirable new product, they may perceive
reasons to overstate their [willingness-to-pay]."
That people were less sensitive to changes in Cash when the steak
decision task was nonhypothetical means, holding the magnitude of other
parameters constant, that the computed amount of money required to make
an individual indifferent between two options that differ in the level
of an attribute (e.g., marginal willingness-to-pay) would be larger in
the IC mechanism than the traditional hypothetical approach. This
finding may initially seem counter-intuitive, as most studies find
higher willingness-to-pay in hypothetical versus real treatments. Note,
first, however, that whether price sensitivity should increase or
decrease when a task is made IC is theoretically ambiguous. On one hand,
people might be expected to become more price sensitive with an IC
mechanism as they will actually receive the cash. On the other hand,
making a decision task IC might force people to more carefully consider
other product attributes when completing the ranking, since they will
now be taking a meat product home, rather than simply picking the
options with the highest cash offer. Second, it is important to note
that the marginal utility of other attributes is not held constant when
a decision task is made IC. In particular, the disutility associated
with the "no meat" option significantly increases when the
task is IC. This is the same as saying that the utility from having a
steak significantly decreases when the task is IC. This latter result is
exactly what studies such as Lusk and Schroeder (2004) found: the
utility of having a steak falls when the task is real instead of
hypothetical. That the marginal utilities of most of the other steak
attributes (hormone, traceability, and size) are uninfluenced by whether
the decision task is IC is also consistent with Carlsson and Martinsson
(2001) and Lusk and Schroeder (2004), who found little difference in
real and hypothetical marginal utilities for product attributes.
Results in table 2 also indicate that information significantly
affected preference parameters. Providing information about
pasture-grazed beef significantly increased the marginal utility of the
pasture attribute as expected. Interestingly, the marginal effect of
information interacted with the IC-treatment effect for the Size, Cash,
and None attributes. To see this, note that the utility of None can be
written as: -11.873 + 1.289 x Info + 8.082 x Non-Hyp - 5.698 x Info x
Non-Hyp. This implies that when information was provided in the
hypothetical mechanism, the value of having a steak decreased; however,
providing information in the IC mechanism increased the utility of
having a steak.
Turning to the scale function, results reveal that moving from
hypothetical to nonhypothetical rankings increased the scale in the
steak model, which implies that error variance decreased (the p-value
from a two-tailed t-test is only 0.08, but the hypothesis that the scale
factor is greater than zero is rejected at the p = 0.04 level according
to a one-tailed test). This result is consistent with the findings of
Haab, Huang, and Whitehead (1999) and suggests that, holding all else
equal, predicted market shares will be more uniform using hypothetical
responses as compared to IC responses. Providing information in the
steak rankings was associated with an increased error variance. Finally,
for both the steak and ground beef models, we find that the error
variance significantly increased for choices associated with higher
ranks. Apparently, people were more consistent in determining which
options were among the few most desirable as compared to determining the
relative ranking among options of medium to low desirability.
To further investigate the implications of the results, market
share simulations were conducted. The estimates in table 2 were used to
predict the market share that a new pasture-raised product would garner
relative to a traditional beef product. To carry out the simulation,
parameters in table 2 were substituted into the logit formula, assuming
the only products in the choice set were a new pasture-raised product
and a traditional nonpasture raised product. Table 3 reports results
from the market share simulations assuming conventional and pasture-fed
steak (ground beef) were available for sale at $8.00/lb ($2.25/lb) and
$10.00/lb ($4.25/lb), respectively. The first column of results shows
the predicted market share using estimates from the IC, nonhypothetical
mechanism. Results indicate that the pasture-fed product would be
expected to achieve about 52% market share in the steak market and 56%
in the ground beef market. These results contrast sharply with the
market share estimates from the hypothetical treatment, which predicts
that pasture-fed beef would only achieve about 39% market share in the
steak market and 42% market share in the ground beef market. The 95%
confidence intervals suggest that this is a statistically significant
difference in predicted market shares for pasture-raised steaks, but not
for ground beef. Obviously, pasture-raised products do not currently
enjoy market shares as high as those estimated in table 3, and it is
important to recognize that table 3 reports estimates of demand at given
prices and that a host of supply-side factors need be considered to
project an equilibrium quantity sold.
Conclusions
Although conjoint analysis is one of the most popular marketing
research tools, it suffers from a potentially serious shortcoming: the
method is not incentive compatible. This paper introduces a conjoint
ranking mechanism that overcomes this shortcoming. The mechanism
requires people to rank a set of product profiles, where a profile that
is assigned a lower rank is more likely to be purchased. The method of
implementation used in this article involved subjects placing cards
containing descriptions of the product profiles on various sized slices
of a wheel, which was subsequently spun to determine the product that
was ultimately received.
The new mechanism was investigated in an empirical application
related to consumer preferences for beef attributes. Results reveal that
the consumers' preferences for ground beef were statistically
indistinguishable when ranking products with the new incentive
compatible mechanism and ranking products in a traditional hypothetical
format. The fact that no differences were observed may be attributable
to the fact that ground beef is a low-valued good and the opportunity
cost of deviating from rational behavior is relatively small. This line
of reasoning is supported by the additional finding that providing
people information about pasture raised beef did not affect preferences
for that attribute when evaluating ground beef. In contrast to the
low-valued ground beef products, the new, nonhypothetical mechanism
significantly influenced rankings of steaks. In particular, people were
less sensitive to price changes in the incentive compatible mechanism
than they were in the hypothetical rankings. Further, people tended to
overstate their utility of having a steak in the hypothetical rankings
as compared to the incentive compatible approach. Results also reveal
that the error variance of the random utility function was significantly
lower when the decision task was nonhypothetical. Finally, we found that
the forecasted market share of a new pasture-raised steak was
significantly lower in the hypothetical ranking as compared to the
forecast from the incentive compatible mechanism.
Although conjoint ranking methods have the potential to provide
much more information about people's preferences than conjoint
choice methods, our results reveal this information advantage is
partially offset by the fact that less information is conveyed about
people's preferences for less preferred, higher ranked options as
compared to the more preferred, lower ranked options. The next step in
our research program is to determine which implementation method
(choices versus ranking) and mechanism (hypothetical or nonhypothetical)
best predicts actual retail shopping behavior.
The authors would like to thank Bailey Norwood for his suggestion
of the use of a spinning wheel to implement the incentive compatible
ranking mechanism.
[Received September 2006; accepted September 2007.]
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(1) To date, most applications of IC preference elicitation methods
have involved experimental auctions. Lusk and Shogren (2007) show that
more than 100 academic studies have been conducted using IC auctions to
value new goods and services; however, to date such auction methods have
not gained the widespread popularity among marketing academics and
professionals as has conjoint analysis.
(1) To date, most applications of IC preference elicitation methods
have involved experimental auctions. Lusk and Shogren (2007) show that
more than 100 academic studies have been conducted using IC auctions to
value new goods and services; however, to date such auction methods have
not gained the widespread popularity among marketing academics and
professionals as has conjoint analysis.
(2) In principle, any function in which the probability of
receiving a product is monotonic in the assigned rank would be suitable;
the function presented here is a particularly easy to implement.
(3) If it is desirable to let respondents express indifference
between product profiles, the mechanism described in this section can be
easily modified simply by letting people assign two products the same
rank and re-scaling the probabilities to sum to one. In practice, this
is easily handled by leaving one of the slices on the wheel blank and
re-spinning the wheel if it happens to land on the blank slice.
(4) If people only cared about receiving additional money and not
about the meat products, this would be reflected in our econometric
results by finding the estimated utility derived from the amount of cash
provided with the "no meat" option outweighing the disutility
of having no meat; as we show later in our results, this is not the
case.
(5) We also investigated whether [[rho].sub.1m] was rank
dependent--i.e., whether the error-variance effect resulting from moving
from non-IC rankings to IC rankings depended on the rank. We could not
reject they hypothesis that the IC treatment effect in the scale
equation was the same for initial ranks as it was for the latter ranks
according to a likelihood ratio test (p-values were 0.17 for the steak
model and 0.47 for the ground beef model).
Jayson Lusk is professor and Willard Sparks Endowed Chair,
Department of Agricultural Economics, Oklahoma State University, and
Deacue Fields and Walt Prevatt are associate professor and professor,
respectively, both in the Department of Agricultural Economics, Auburn
University.
Table 1. Meat Attributes and Attribute Levels Used
in Conjoint Study
Attributes Attribute Levels
Pasture feed Cattle grazed in pasture only
(nothing mentioned about how
animal was fed)
Antibiotic and Cattle raised without antibiotics,
hormone use no growth hormones added
(nothing mentioned about
growth hormones or antibiotics)
Traceability Cattle traceable back to farm
(nothing mentioned about
traceability)
Size 1 1-lb steak (or 1-lb ground beef)
21-lb steaks (or 2-lbs ground
beef)
Cash offered $3 (or $1 if ground beef)
$5 (or $2 if ground beef)
$7 (or $3 if ground beef)
$9 (or $4 if ground beef)
Table 2. Rank-Ordered Logit Estimates
Ground Beef
Parameter Std. Error
Variable
Pasture 1.071 *** (a) 0.167
Hormone 1.237 *** 0.254
Trace 0.972 *** 0.196
Size 0.616 *** 0.240
Cash 0.696 *** 0.144
None -6.763 *** 0.882
Info * Pasture 0.257 1.013
Info * Hormone 0.341 1.235
Info * Trace -0.407 0.513
Info * Size -0.643 ** 0.321
Info * Cash