Identification of Dynamic Models of Rewards Programme

'Frequent-buyer' type of rewards program is a commonly used marketing tool for companies to compete for market shares. It also provides an unique environment for studying consumer's forward-looking behavior. The consumer's problem on accumulating reward points can be formulated as a stationary infinite horizon discrete choice dynamic programming (DDP) 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 reward points). We discuss how this identification result is related to the goal-gradient hypothesis studied in the consumer psychology literature