Probabilistic versus random-utility models of state dependence: an empirical comparison

Abstract

Brand choice models estimated on scanner panel data typically show that a household's brand choice process is characterized by state dependence, i.e. a household's brand choices are serially correlated over time. Two approaches have been employed by marketing researchers to estimate state dependence effects using brand choice data. The first approach is based on probability models—such as Markov Chains and Linear Learning Models—that directly allow a household's brand choice probabilities to be temporally correlated. The second approach is based on random utility models—such as the Multinomial Probit with serially correlated error terms—that allow a household's latent utilities for brands to be temporally correlated, and then derive the household's brand choice probabilities as the first-order conditions for the household's utility-maximization problem. The random utility approach has acquired prominence in recent years given the increasing influence of economic models, and hence a utility-based view of consumer decision-making, in marketing. However, the first approach has served a fruitful role for over four decades in terms of accurately tracking and predicting brand choices. In this study, we explicitly compare a probabilistic model versus a random utility model of state dependence both in terms of their ability to explain and predict observed brand choices of households, and in terms of the marketing mix elasticities that they yield. We estimate both models using scanner panel data on households' purchases in four different categories of packaged goods. Using either model, we quantify significant state dependence effects along two dimensions. Interestingly, despite the differences in their mathematical foundations, we find both models to be remarkably similar in terms of predicting observed brand choices and in terms of the their recovery of marketing-mix elasticities.