Identification of Dynamic Models of Rewards Program

Abstract

'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. In particular, the consumer's problem can be formulated as a stationary infinite horizon discrete choice dynamic programming (DDP) model. We study the identification issue of this dynamic model of rewards program. To illustrate our identification arguments, we use a simple dynamic store choice model where stores offer 'frequent-buyer' type reward programs. We show that the parameters of this model, including the discount factor, are well-identified. We also discuss the connection between our model and the goal-gradient hypothesis proposed in the psychology literature.