Identification of Dynamic Models of Rewards Programme

“Frequent-buyer” rewards programmes are commonly used by companies as a marketing tool to compete for market share. They provide a unique environment for studying consumers’ forward-looking behaviour. The consumer's problem on accumulating reward points can be formulated as a stationary infinite horizon discrete choice dynamic programming model. We show that the parameters of this model, including the discount factor, are well-identified. In particular, it is possible to identify state-dependent discount factors (i.e. discount factors can vary with the number of reward points). We discuss how this identification result is related to the goal-gradient hypothesis studied in the consumer psychology literature.