An incentive compatible conjoint ranking mechanism.

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.