Base Model: the Random Parameter Logit Model and WTP

Table 5.6 presents the estimation results for the base model using the Random Parameter Logit (RPL) model, which is used to capture consumers‘ preference heterogeneity. Compared with the results of the CL model in Table 5.2, according to the LR test the goodness of fit of this model has a significant improvement in terms of the values of the Log Likelihood Function (- 5275.028 in Table 5.2 v.s. -3845.335 in Table 5.6) and the Pseudo-R2 (0.25 in Table 5.2 v.s. 0.531 in Table 5.6). As explained in Chapter 4, the values of the estimated parameters are fixed in the Conditional Logit model. In the RPL model, however, the estimated parameters are continuous and follow a certain distribution, and the density of the parameters can be specified to be normal or some other distribution (Train, 2003). There are two sets of estimated parameters in a RPL model. One set includes the estimated random/fixed parameters of the examined attributes,

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and the other set represents the standard deviations of the random parameters as shown in Table 5.6.

Table 5.6: Base Model: RPL and WTP Estimates

Variable Coefficient t-ratio WTP

($/2 litres)

t-ratio

Mean value of Random parameters in utility function

Omega-3 1.300*** 6.539 0.524*** 6.658

Risk Reduction Claim 1.043*** 7.106 0.420*** 7.200

Disease Prevention Claim 1.034*** 6.833 0.416*** 6.913

Heart Symbol 0.313*** 4.653 0.126*** 4.685

Government Verification 0.903*** 8.225 0.364*** 8.359

Third Party Verification 0.547*** 5.428 0.220*** 5.476

Mean value of Fixed parameters in utility function

Price -2.483*** -37.198 - -

Function Claim 0.316** 2.162 0.127** 2.161

No Purchase -9.214*** -44.364 -3.711*** -93.638

Standard deviations of random parameters

Sd-Omega-3 4.046*** 22.490 - -

Sd-Risk Reduction Claim 0.641*** 4.067 - -

Sd-Disease Prevention Claim 1.258*** 9.754 - -

Sd-Heart Symbol 0.525*** 4.374 - -

Sd-Government Verification 1.104*** 7.792 - -

Sd-Third Party Verification 0.663*** 3.453 - -

Log Likelihood Function = -3845.335; Pseudo-R2 = 0.531

*,** and *** indicate significant at the 10%, 5% and 1% levels, respectively.

The estimation results in Table 5.6 are generally consistent with the results in Table 5.2 for the examined attributes. All random and fixed parameters are highly significant and with the expected signs. Consumers prefer all three types of health claims relative to no health claim (base level). They also prefer a heart symbol (partial labelling) to be present on food labels relative to no symbol. The respondents also prefer the verifications of health claims by government or third party compared with no verification (base level). They respond positively to

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milk enriched with Omega-3. Not buying any milk product or paying a higher price decreases their utilities.

However, some differences exist in terms of WTP estimations in the two models presented in Tables 5.2 and 5.6. First, when the base model is estimated by the Random Parameter Logit model in Table 5.6, consumer‘s WTP for government verification is 36 cents for a two-litre carton milk, which is significantly higher than their WTP for third party verification at 22 cents, indicating that government verification has a bigger impact on consumers‘ utilities than third party verification when heterogeneity of preferences is taken into account. In contrast, the model presented in Table 5.2 was unable to detect a significant difference between consumers‘ WTP for these two verification organizations. Second, the WTP values for a risk reduction claim and a disease prevention claim are close to each other, at about 42 cents for a two-litre carton of milk in the RPL model (Table 5.6). However, in the CL model (Table 5.2), consumers‘ WTP for a risk reduction claim is significantly higher than for a disease prevention claim. Third, consumers‘ WTP for Omega-3 in Table 5.6 is higher than in Table 5.2. These differences are the results of using different estimation methods. The fixed coefficients in the CL model can only estimate average values which assume that respondents‘ preferences are homogenous, while the random parameters in the RPL model allow for heterogeneity of preferences which tends to be more realistic. The goodness of fit of the RPL model is also better than the CL model.

The estimated standard deviations of the random parameters are all highly significant, which further indicates that it is necessary to include a mixed structure for the selected parameters in the CL model to improve the goodness of fit of the model. The significant standard deviations of the random parameters indicate that strong variations exist in consumers‘ preferences for whether the milk product is enriched with Omega-3, whether there is a risk

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reduction claim or a disease prevention claim on food labels, whether a heart symbol is present, and whether there is government or third party verification of the health claims.

The random parameters of the RPL model further identify the distribution of individual taste preferences in the population. For example, for a normal distributed parameter, which has a positive (negative) mean estimate, the share of respondents who have a positive (negative) view of that attribute can be calculated. Following Train (2003) and Hu, Veeman and Adamowicz (2005), for a random parameter β ~ N(b, σ2_{), the probability of β < 0, equals Φ[(0-b)/σ]. Φ (β | b,}

σ2_{) is the normal density of the standard normal distribution. The probability of β > 0, equals 1-}

Φ[(0-b)/σ]. The interpretation of the probabilities of β < 0 (> 0) is the percentage/share of respondents who have a negative (positive) view of an attribute. The RPL estimation results in Table 5.6 were obtained by assuming a normal distribution of the random parameters for the variables Omega-3, Risk Reduction Claim, Disease Prevention Claim, Heart Symbol, Government Verification and Third Party Verification. Table 5.7 reports respondents‘ heterogeneous preferences for the attributes with random parameters.

Table 5.7: Respondents‟ Heterogeneous Preferences for the Attributes with Random Parameters

Variable Positive Percentage Negative Percentage

Omega-3 62.55% 37.45%

Risk Reduction Claim 94.84% 5.16%

Disease Prevention Claim 79.39% 20.61%

Heart Symbol 72.57% 27.43%

Government Verification 79.39% 20.61%

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In total, 62.55% of the respondents have positive views (37.45% with negative views) of the Omega-3 attribute, indicating that about two thirds consumers prefer the milk products containing Omega-3. The majority (94.84%) of respondents value a risk reduction claim positively relative to no health claim. There are 79.39% of respondents who value a disease prevention claim positively relative to no health claim. The heart symbol attribute is positively viewed by 72.57% of respondents. There are 79.39% and 79.67% of respondents who have positive values for government verification and third party verification, respectively, indicating that most consumers prefer government or third party verification relative to no verification. Clearly the respondents have different percentages of positive views (ranging from 62.55% to 94.84%) for the attributes listed in Table 5.7, indicating different degree of heterogeneity in consumers‘ responses to these attributes.