A First-Passage Time Model for Predicting Inactivity in a Contractual Setting
34 Pages Posted: 5 Jul 2007 Last revised: 4 Apr 2012
Date Written: November 17, 2010
A central focus of database marketing is on predicting customer defection (churn). We argue this focus would be better placed on predicting when customers become inactive, which often precedes the time at which the customer terminates the contract, and represents a behavioral regularity found across several contractual markets. We model customers' usage (consumption) paths, and whether customers become inactive, as realizations from a single continuous-time stochastic process with an absorbing state. Our context is usage of a cellphone service. In addition to robust predictions, the model has two managerially important parameters, drift and volatility, and offers several advantages over existing methods. First, it can be calibrated at the individual level and before is observed. Second, based on these parameters, the model provides unique insights into who managers should intervene with to prevent customer churn. An appealing feature of our model for managers is that it is also easily implementable in a platform such as Excel. These features make the proposed model useful as an early warning system for a service provider to guide policy on customer retention.
Keywords: defection, churn, stochastic models, brownian motion, first hitting time
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