"How to Project Customer Retention" Revisited: The Role of Duration Dependence. Issue 1 (August 2018)

• Record Type: Journal Article
• Authors: Fader, Peter S.; Hardie, Bruce G.S.; Liu, Yuzhou; Davin, Joseph; Steenburgh, Thomas
• Is Part Of: Journal of interactive marketing. Volume 43:Issue 1(2018)
• Page Start: 1
• Page End: 16
• Publication Date: 2018-08
• Subjects: beta-geometric (BG) distribution -- beta-discrete-Weibull (BdW) distribution -- retention rate dynamics; Direct marketing -- Periodicals; Internet marketing -- Periodicals; 658.87
• DOI: 10.1016/j.intmar.2018.01.002
• Languages: English
• ISSNs: 1094-9968

Abstract

Cohort-level retention rates typically increase over time, and the beta-geometric (BG) distribution has proven to be a robust model for capturing and projecting these patterns into the future. According to this model, the phenomenon of increasing cohort-level retention rates is purely due to cross-sectional heterogeneity; an individual customer's propensity to churn does not change over time. In this paper we present the beta-discrete-Weibull (BdW) distribution as an extension to the BG model, which allows individual-level churn probabilities to increase or decrease over time. In addition to capturing the phenomenon of increasing cohort-level retention rates, this new model can also accommodate situations in which there is an initial dip in retention rates before they increase (i.e., a U-shaped cohort-level retention curve). A key finding is that even when aggregate retention rates are monotonically increasing, the individual-level churn probabilities are unlikely to be declining over time, as conventional wisdom would suggest. We carefully explore these connections between heterogeneity, duration dependence, and the shape of the retention curve, and draw some managerially relevant conclusions, e.g., that accounting for cross-sectional heterogeneity is more important than accounting for any individual-level dynamics in churn propensities.