History Dependent Brand Switching: Theory and Evidence

We present a model of brand-switching in which a consumer's impression of each brand is based on her memory of past consumption of this brand, and is stochastically updated whenever the brand is consumed. In the ordinal version of the model, consumer's memory is an ordering of the available brands. The top brand is chosen and consumed, and may therefore move to a different ranking. In the cardinal version, the consumer remembers a "cumulative utility index" per brand, and, when a brand is consumed, the index is updated by the addition of a random variable, interpreted as "instantaneous utility." In both versions of the model it may be assumed that the consumer may sometimes be "dormant," choosing the same brand out of inertia, or that she is always "active," re-evaluating her decision based on her cumulative memory. We prove that, in all versions, the frequencies of choice converge, with probability 1, to limit frequencies which can be computed from the model's parameters. We also show that, under mild assumptions, every sequence of choices would have a positive probability. We test the ordinal model empirically, using scanner data on purchases of crackers, yogurts, and catsups. We show that both the "order effect" and the "inertia effect" exist. Specifically, the ordinal model performs significantly better than its restricted version, in which only the last brand is recalled. Similarly, the model performs significantly better with the inertia assumption than without it.