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A Bivariate Timing Model of Customer Acquisition and Retention

School of Business, University of Wisconsin, Madison, Wisconsin 53706
Department of Marketing, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Wharton Small Business Development Center, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
dschweidel{at}bus.wisc.edu
psfader{at}wharton.upenn.edu
ebradlow{at}wharton.upenn.edu

Two widely recognized components, central to the calculation of customer value, are acquisition and retention propensities. However, while extant research has incorporated such components into different types 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 value of prospects and customers.

To accomplish these tasks, we use a bivariate timing model to capture the relationship between acquisition and retention. Using a split-hazard model, we link the acquisition and retention processes in two distinct yet complimentary ways. First, we use the Sarmonov family of bivariate distributions to allow for correlations in the observed acquisition and retention times within a customer; next, we allow for differences across customers using latent classes for the parameters that govern the two processes. We then demonstrate how the proposed methodology can be used to calculate the discounted expected value of a subscription based on the time of acquisition, and discuss possible applications of the modeling framework to problems such as customer targeting and resource allocation.

Key Words: customer acquisition; customer retention; customer relationship management; stochastic models
History: Received: May 2, 2006;