We tested an array of specifications before the MLM and LCM were finalized and presented in Tables 6 and 7. Comparison of the McFadden R2 and log-likelihood scores reveal that both the MLM and LCM are superior in explanatory power than the CLM. The CLM recorded a McFadden R2 of 0.1535 compared to 0.3437 in the MLM and 0.3641 in the LCM. Thus, we can confidently reject the CLM in favor of the MLM and LCM.
The diagonal values the Cholesky matrix (Table 8) identified the presence of taste heterogeneity within the tested attributes (Hensher et al 2005). These diagonal values revealed that significant taste heterogeneity in all eight coefficients specified as random parameters in the model. Multiple significant values in the off-diagonal elements of the Cholesky matrix suggest that significant correlation exist between the attributes, thus justifying the specification of joint distribution.
Results from the Mixed Logit Model
Consumers’ relative WTP for Australian and Canadian steak were calculated for nine selected consumer profiles based on their age, education, income, and gender. For brevity, we tied education to income as these factors tend to be positively correlated and the shopper's gender is assumed to be female.
The relative WTP follows interpretation of dummy variable, where the base case is the U.S. labeled steak. The WTP is calculated as a negative ratio, where the nominator is the combination of the estimated mean values of the coefficients associated with a particular country (θcountry) and its interaction effect (γ’country×d) and the denominator is the fixed price coefficient (αprince).
Table 9. Willingness-to-pay estimations of selected profiles following mixed logit model
| ||Canadian steak||Australian steak|
|Higher income, higher education|| || || || |
|Income =$80k, education = 16 yrs|| || || || |
| Age = 35.3||−3.89***||0.53||−5.99***||0.66|
| Age = 45.0||−4.51***||0.45||−6.49***||0.56|
| Age = 56.62||−5.24***||0.41||−7.10***||0.52|
|Sample average income and education|| || || || |
|Income =$52.37k, education = 14 yrs|| || || || |
| Age = 35.3||−4.71***||0.48||−7.29***||0.60|
| Age = 45.0||−5.33***||0.39||−7.80***||0.49|
| Age = 56.62||−6.07***||0.36||−8.40***||0.45|
|Lower income, lower education|| || || || |
|Income =$30k, education = 12 yrs|| || || || |
| Age = 35.3||−5.51***||0.54||−8.52***||0.67|
| Age = 45.0||−6.13***||0.47||−9.03***||0.59|
| Age = 56.62||−6.86***||0.45||−9.64***||0.56|
Not surprisingly, the results revealed that on average, imported steak is less preferred by consumers across all education, income, and age levels. The discounts (or negative WTP) calculated at the sample mean level of age (56.62 years), education (14 years), and income ($52.37K) were $6.07/lb and $8.40/lb on average for Canadian steak and Australian steak, respectively, when compared to steak from the United States. These estimates suggest that high-value imported beef are likely to encounter less favorable receptions from U.S. conusmers with the new mandatory COOL rule.
The magnitude of the discount indicated Canadian steak is preferred over Australian steak. We found that older consumers are less willing to pay for imported steak; similar observations of older consumers aversion toward imports were also reported in Alfnes (2004) and Loureiro and Umberger (2007). The magnitude of the discount decreased as education and income level of the shopper increased. For example, the average discount on the Canadian steak was $3.89 for a 35.3-year-old female shopper with household income of $80,000 and 16 years of education. The discount increases 41% to $5.51 for a same-aged female shopper with household income of $30,000 and 12 years of education.
The negative WTP for imported steak suggests that holding other factors constant, most consumers need to be compensated, either in price or in favorable attributes, for choosing Canadian or Australian strip loin steak over U.S. strip loin steak. One such strategy is to incorporate some additional quality features into imported steaks. Table 10 presents the marginal WTP of the non-country-of-origin attributes. The WTP is calculated as the negative ratio between the coefficient of an attribute to the price coefficient. On average, the marginal WTP for BSE-tested beef, traceable beef, or with both attributes combined were $5.70, $5.85, and $8.05, respectively; the WTP for these food-safety enhancements eclipse a large portion of the discount associated with country-of-origin for most consumers. In addition, the tenderness-assured steaks garner a premium of $4.08 on average. Although natural steak was not found to be associated with significant WTP, overall, the food-safety and eating-quality attributes might provide a viable way to differentiate imported steak from domestic products.
Table 10. Marginal willingness-to-pay estimates from mixed logit model
| ||Coef. $/lb||S.E.||95% C.I.|
|BSE|| 5.70***||0.3306|| 5.05||6.35|
|TRACE|| 5.85***||0.3307|| 5.20||6.50|
|BSE_TRC|| 8.05***||0.3642|| 7.33||8.76|
|TENDER|| 4.08***||0.2068|| 3.68||4.49|
|NAT|| 0.18 ||0.1884||−0.19||0.55|
Results from the Latent Class Model
The LCM provides a different perspective from the MLM. As noted, the model yielded five unique classes. We found that age, income, and education are significant in determining the latent class an individual belongs to (see Table 7). As with the MLM, coefficient estimates of the attribute variables from the LCM were best interpreted in the context of WTP. The average WTP for an attribute within a consumer class q is the negative ratio between an attribute coefficient in that class q (βattribute,q) and price coefficient in the same class q (αprince, q). The standard deviation of the WTP measure was simulated using the Krinsky and Robb (1986) procedure with 2,000 replications.
As with the MLM, the LCM also showed wide-ranging taste heterogeneity for country-of-origin and other attributes. Of particular interest is the discount needed (or negative WTP) to switch from U.S. steak to imported steak. From Table 11, the discount needed for Australian steak ranged from as little as $1.09/lb to a prohibitive $49.48/lb across different classes, holding other factors constant. Similarly, the discount needed for Canadian steak, across all class membership, ranged from $0.74/lb to $35.12/lb. The higher values of the WTP range suggest that a significant portion of consumers are likely to avoid imported steak.
Table 11. Willingness-to-pay estimates from the latent class model
| ||Class 1 Nonconsumer ($/lb)||Class 2 Anti-imports consumers ($/lb)||Class 3 Food-safety conscious consumers ($/lb)||Class 4 Value-seekers ($/lb)||Class 5 Strip loin lovers ($/lb)|
|Would-not-buy option|| 6.67***||−12.10***||−2.91***||−6.25***||−33.60***|
|AUS||−7.28***||−49.48***||−4.92***|| −1.09***|| −6.18***|
|CAN||−6.64***||−35.12***||−3.22***|| −0.74***|| −4.74***|
|BSE|| 5.33***||4.07*|| 8.95***|| 1.66***|| 7.39***|
|TRACE|| 5.83***||3.65*|| 9.40***|| 1.85***|| 6.86***|
|BSE_TRC|| 6.45***|| 9.17***|| 12.83***|| 2.22***|| 11.17***|
|Tender|| 3.41***|| 11.16***|| 5.86***|| 1.06***|| 5.26***|
Overall, the marginal WTP estimations for BSE, TRACE, BSE_TRC, and TENDER revealed positive consumer interest in these attributes. Except for consumers in one class, natural beef was generally not regarded as an attractive attribute.
Of the five segments, only consumers in the first segment exibited postive WTP value for the would-not-buy coefficient that captured the utility/disutility yielded from not purchasing the steak. With the positive WTP value, these consumers disliked the strip loin steaks outlined in the choice experiment. These consumers could be vegetarians or did not prefer the particular cut of beef. For this reason, this class of consumers were labeled as non-steak consumers. They accounted for about 16% of the sample. Interestingly, even individuals who generally did not prefer the strip loin steak, if they were to make a choice, they would still choose an U.S. product with almost all other quality guarantees/assurances (except for natural). Estimates of the class membership determinant coefficients in Table 7 indicated that female and older consumers were more likely to be in this class.
The second segment accounted for 17% of the sample. These consumers were labeled as anti-imports consumers for displaying strong aversion toward imported steaks. The estimated discount needed for this group to switch from U.S.-origin steak to Australian and Canadian steak were $49.48/lb and $35.12/lb, respectively. Further, these consumers were found to be willing to pay more for tenderness than for BSE-tested and traceable steak; this implied, they valued eating-quality attributes more than food-safety attributes. The class determinant estimates revealed that female, older, or less educated consumers were more likely to be in this class.
The third group was categorized as food-safety conscious consumers. Even though they displayed moderate aversion toward imported steak, they had the largest WTP for food-safety attributes among all the groups. Interestingly, they were willing to pay a small premium for natural beef, which was insignificant in the CLM, the MLM, and the other classes in the LCM. This group constituted the largest segment, accounting for 27% of the sample. Older consumers were found to be more likely to be in this segment.
We observed the lowest discount on the imported steaks ($1.09 for Australian and $0.74 for Canadian) on value-seekers in segment 4. This segment accounted for 17% of the sample. Individuals in this segment exhibited the lowest WTP for all other attributes examined. Of all the segments, this group was the least likely to be affected by the COOL mandate. The class assignment estimates suggested older and higher educated consumers were more likely to belong to this class.
Consumers in the fifth segment were willing to pay a modest amount to avoid imported steak and for the non-COOL attributes. This group had the largest disutility associated with not buying the steak (−$33.60), as reflected by the negative WTP associated with the would-not-buy. Hence, this group is labeled as strip loin steak lovers. They accounted for 24% of the sample.
From the country-of-origin WTP within the LCM, only the value-seeking consumers in segment 4 appeared to be willing to make the trade-off between domestic and imported steaks with a modest WTP. The remaining 83% of the sample required at least $4.92/lb and $3.22/lb discounts for consuming Australian and Canadian steak. These findings reiterate the possibility of COOL exerting downward pressure on both the price and quantity demand for imported beef.