Choosing brands: fresh produce versus other products.

Of course, there are some confounding factors including demographic characteristics attributed to the differences of WTP for brands across product categories. To investigate whether the WTP for brands is still sensitive to product categories, we conduct econometric estimation to control for the relevant sociodemographic variations.

Econometric Estimation and Discussion

The underlying WTP for brands of product category k that is denoted by [W.sup.*.sub.ik] for consumer i is not completely observable to researchers. Instead, we conduct survey and collect the perceived nonnegative value and the range of WTP for brands of each product category. Let [IW.sub.ik] and [W.sub.ik] denote the perceived range of WTP and the perceived point WTP for brands of product category k for consumer i. To fully utilize the survey data, we investigate both [IW.sub.ik] and [W.sub.ik].

Furthermore, we assume that the latent WTP is linear for all relevant explanatory variables,

(8) [W.sup.*.sub.ik] = [beta]'X + [[mu].sub.i] + [[epsilon].sub.ik]

where X = [[IP.sub.k], [Z.sub.i], [IPREF.sub.k]] is a covariate matrix, B's are associated coefficients, and [[mu].sub.i] and [[epsilon].sub.ik] are components of error terms. [IP.sub.k] for k = 1, 2, 3, 4 are the product category dummies that capture the effects of product attributes. People prefer brands for different reasons due to the nature of product attributes and consumers' idiosyncratic characteristics. The product category dummies will allow for testing and quantifying the results of inequality (6), in particular, to quantify how much lower the WTP is for fresh produce than other products. [Z.sub.i] consists of the relevant socio-demographic characteristics of an individual consumer i. We introduce household income per member in thousand dollars (inc) and its quadratic term ([inc.sup.2]), age (age) and its quadratic term ([age.sup.2]), education indicators (edu1 and edu2), where edu1 equals one for respondents with bachelor's degree or higher and zero otherwise and edu2 reflects whether a respondent is currently enrolled in college, gender dummy (gender), race dummies, and household size (hsize). [IPREF.sub.ik] = 1 indicates that consumer i has a strong brand preference for product k, and zero otherwise. Table 2 shows that brand-preferring respondents are willing to pay more than their counterparts for brands of any product category. Hence, we expect a positive sign of [IPREF.sub.ik]. [[mu].sub.i] and [[epsilon].sub.ik] depict individual heterogeneity among consumers and idiosyncratic disturbances, respectively.

Econometric Estimation Based on [W.sub.ik]

Suppose researchers observe a nonnegative value of the perceived WTP,

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [W.sup.*.sub.ik] is given in equation (8). We conduct six estimation analyses on [W.sub.ik], including OLS, tobit, and random-effect tobit (RE-Tobit) models with and without brand preference. The estimation results are reported in table 4. Before we move on to the detailed discussion of estimation results, we report some test results on model specifications.

* Testing for endogeneity of brand preference: We are aware of the endogeneity problem of brand preference. Unfortunately, we do not have good instruments to control endogeneity. Nevertheless, we check robustness by running regressions with and without the brand preference dummy, and results are robust.

* Testing for heteroskedasticity, including the Breusch-Page test and the unrestricted White test in the OLS regressions: Our results reject the null hypothesis of homoskedasticity at the 1% significance level for the OLS models with or without brand preference. Hence, we report heteroskedasticity-consistent standard errors for the OLS models.

* Testing for the presence of individual heterogeneity: If the model does not actually contain the individual heterogeneity, the panel estimator is not significantly different from the pooled estimator. The absence of an individual heterogeneity effect is statistically equivalent to [H.sub.0] : [[sigma].sup.2.sub.[mu]] = 0 (Wooldridge 2002, p. 264). A likelihood ratio test for [H.sub.0] : [[sigma].sup.2.sub.[mu]] = 0 rejects the null hypotheses at the 1% significance level ([chi square](1) = 192 and [chi square](1) = 185 with or without brand preference, both having a zero p-value). Hence, the RE-Tobit estimation is more appropriate than the tobit estimation on the pooled data.

Table 4 shows that the results of the six models on [W.sub.ik] are qualitatively similar and robust. Based on the tests discussed above, we report the marginal effects and discuss the estimation results based on the RE-Tobit model with brand preference.

We found that consumers are willing to pay 5-6% more for brands of electronics, clothing, and packaged food than in fresh produce after controlling for brand preferences, and 9-10% without controlling for brand preference. The results confirm that consumers are willing to pay substantially less for brands in fresh produce than other product categories after controlling for sociodemographic variations. The empirical results also support our expectations regarding the impacts of sociodemographic factors on WTP for brands. In particular:

* The income per household member increases the WTP for brand products, while the marginal increase declines as income goes up in the OLS estimations. However, the marginal effect of income is minimal.

* An increase in age decreases the WTP for brands while the marginal effect of age increases as age goes up. The results suggest that both younger and elder respondents are more likely willing to pay for brands than the rest of the population.

* Females are willing to pay approximately 5% more for brand products than males.

* Less educated people have a 7% higher stated WTP for brands than more educated individuals.

* White respondents have significantly smaller WTP for brands compared with other ethnic groups. Among all ethnic groups, African Americans have the highest stated WTP for brands--19% more than white respondents.

* The intensity of preference for brand products affects the level of WTP. Consumers with stronger brand preference are willing to pay approximately 16% more for brand products than their counterparts.

Econometric Estimation Based on [IW.sub.ik]

Rather than using the double-bounded contingent valuation method approach (Hanemann, Loomis, and Kanninen 1991) to directly estimate WTP, we use the ordered probit (OPROBIT) model to investigate the impacts of product category and demographic variations on the WTP for brands. The OPROBIT model is built around a latent regression as in the tobit model except the OPROBIT has an ordered categorical dependent variable. The OPROBIT model assumes that the underlying WTP denoted by [[W.sup.*.sub.ik] in equation (8) is unobservable, and respondents' choices of the WTP ranges denoted by [IW.sub.ik] are observable to researchers. In this case, the ordered categorical choice of the WTP ranges between six intervals, 0-20%, 20-40%, 40-60%, 60-80%, 80-100%, and at least 100%,

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where the C's are unknown parameters to be estimated together with [beta]'s in equation (8). The probability of having [IW.sub.ik] = j is the probability that [W.sup.*.sub.ik] lies between a pair of cut points, [C.sub.j-1] and [C.sub.j]. Let [PHI](*) denote the standard normal cumulative distribution function. We have the following probabilities,

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The results presented in table 5 suggest that results are robust with or without incorporating brand preference. Hence, we only report the marginal effects and discuss the results based on the OPROBIT model with brand preference. The comparison of the observed and predicted frequencies for each WTP range in the bottom part of table 5 suggests that overall the OPROBIT models fit data well. For example, 45.70% of respondents indicate that their WTP is less than 20%, and the OPROBIT model predicts 45.01% of such respondents. Similar to the tobit panel estimation on the perceived WTP, the OPROBIT model suggests the following results: (a) respondents' WTP for brands in fresh produce is significantly less than in electronics, clothing, and packaged food; (b) age has a negative effect at an increasing rate on the WTP range; (c) more educated consumers have a lower WTP range than less educated; (d) female respondents likely have a higher WTP level than males; and (e) white respondents are likely less willing to pay more for brands than other ethnic groups including African-American, Asian, and Hispanic respondents.

Marketing Implications with Simulated Brand Premiums

Our results so far show that consumers have a lower WTP for brands of fresh produce compared with electronics, clothing, and packaged food regardless of whether the sociodemographic variations are controlled for. The lower WTP for brands of fresh produce can be a driver for either a low brand price premium or a small market share, or both. In order to identify the likely consequence, we simulate the price premium and the corresponding market share in this section.