An analysis of count data models for the study of exclusivity in wine consumption

Abstract

Several models which analyse count data have been proposed in econometric literature. These models allow the discrete, nonnegative nature of specific phenomena of interest to be gathered in a appropriate way and can be useful for the explanation of specific preference structures among individuals. In this work, an analysis of the number of wine types consumed by residents of Tenerife is carried out, with an aim to observe which characteristics determine the exclusivity in its consumption, given the current context of increased competition in this sector. The specific characteristics of the considered variable allow the study to cover two aspects. The first is methodological, and is seen by the variety of models that may be considered in this case. This focus consists in comparing several possibilities, which fit the type of count data involved. The second aspect is clearly empirical, and is based on the description of not only the most appropriate decision-making mechanism for the study but in the identification of those factors that explain the diversity in wine consumption.

Notes

¹A significant amount of grape diversity is present in the Canary Archipelago, due to several reasons, one of which is the absence of phylloxera.

²Several studies which analyse the influence of socio-economic characteristics on alcohol consumption are Nayga (1996), Su and Yen (2000) and Selvanathan and Selvanathan (2004).

³Note that the log-linear formulation of the parameter λ_i ensures the positive nature of the mean of the dependent variable.

⁴Overdispersion means that the conditional variance is greater than the conditional mean.

⁵The problem of unobserved heterogeneity occurs in application in which behavioural differences among individuals cannot properly ‘captured’ by the group of explanatory variables in the conditional mean function of the model.

⁶This type of model can also be inspired by different approaches. See Boswell and Patil (1970).

⁷This term can pick up a specification error, such as the omission of some explanatory variable (Gourieroux et al., 1984a,b) or by the intrinsic random process (Hausman et al., 1984).

⁸This probability function refers specifically to the NEGBIN II model.

⁹The data base in this study reveals that the number of zeros represents an important percentage (24%) of all observations.

¹⁰Yen (1999) compares continuous and count data hurdle models to study cigarettes consumption by women in the US finding similar demand elasticities with respect to continuous explicative variables.

¹¹Although, in this case the set of explanatory variables is the same, it is possible that it can differ.

¹²Other authors have used different versions of this model, such as the negative binomial (Gurmu and Trivedi, 1996).

¹³Gurmu (1991), Grogger and Carson (1991), Gurmu and Trivedi (1992), among others, have commented on these models. Recent application in order to look for some evidence of the presence of reputation in the return to tourist destination can be found in Ledesma et al. (2005).

¹⁴See Englin and Shonkwiler (1995) for an extension to the Negative Binomial.

¹⁵See Guirao et al. (2001) for a detailed description of the survey.

¹⁶

¹⁷ , where L ₀ is the likelihood function for the restricted model and L ₁ for the unrestricted model.

¹⁸We previously studied the influence of certain socio-economic characteristics of the individual on the number of wine types that are being consumed, but without considering the effect of consumption frequency. In this article the Poisson model was rejected against the two negative binomial estimates using traditional overdispersion tests. This result leads us to consider whether the differences among individuals are not only due to observed heterogeneity but also to unobserved heterogeneity. The unobserved heterogeneity term included in the conditional mean of the negative binomial models can capture the effect of one explanatory variable which has been omitted in the model. The current study includes consumption frequency as the explanatory variable and has not lead to the rejection of the Poisson model against the two negative binomial models. Consequently, we can consider that this variable has assisted in explaining the individual differences that were initially attributed to unobserved heterogeneity, and specifically, to overdispersión.

¹⁹AIC = −2ln L + k; BIC = −2ln L + k ln(N), where L is the maximum likelihood function, k is the number of parameters that are estimated and N is the number of total sample observations.