A Bivariate Timing Model of Customer Acquisition and Retention

Two components central to the calculation of customer value are acquisition and retention propensities. However, while extant research has incorporated such components into different kinds of models, limited work has investigated the kinds of associations that may exist between them. In this research, we focus on the relationship between a prospective customer’s time until acquisition of a particular service and the subsequent duration for which he retains it, and examine the implications of this relationship on the (lifetime) value of customers. To accomplish these tasks, we utilize a bivariate timing model to capture the relationship between acquisition and retention. We incorporate duration dependence into each of the two marginal timing processes, and link them in two ways. First, we use the Sarmonov family of bivariate distributions to allow for correlations in the observed acquisition and retention times; next we allow for latent classes in the parameters that govern the two processes. We then show how the proposed methodology can be used to calculate the discounted expected tenure of service based on the time of acquisition, and discuss possible applications of the modeling framework to problems such as customer targeting and resource allocation.