A Joint Model of Usage and Churn in Contractual Settings

61 Pages Posted: 30 Jul 2011 Last revised: 22 Jan 2017

See all articles by Eva Ascarza

Eva Ascarza

Harvard Business School

Bruce Hardie

London Business School

Multiple version iconThere are 2 versions of this paper

Date Written: April 10, 20112


As firms become more customer centric, concepts such as customer equity come to the fore. Any serious attempt to quantify customer equity requires modeling techniques that can provide accurate multi-period forecasts of customer behavior. While a number of researchers have explored the problem of modeling customer churn in contractual settings, there is surprisingly limited research on the modeling of usage while under contract. The present work contributes to the existing literature by building an integrated model of usage and retention in contractual settings. The proposed method fully leverages the interdependencies between these two behaviors even when they occur in different time frames (as is typically the case in most contractual/subscription-based business settings).

We propose a model in which usage and renewal are modeled simultaneously by assuming that both behaviors reflect a common latent variable that evolves over time. We capture the dynamics in the latent variable using a hidden Markov model with a heterogeneous transition matrix, and allow for unobserved heterogeneity in the associated usage process to capture time-invariant differences across customers. The model parameters are estimated using hierarchical Bayesian methods.

The model is validated using data from an organization in which an annual membership is required to gain the right to buy its products and services. We show that the proposed model outperforms a set of benchmark models on several important dimensions. Furthermore, the model provides several insights that can be very valuable for managers. For example, we show how our model can be used to dynamically segment the customer base and identify the most common “paths to death” (i.e., stages that customers go through before churn).

Keywords: Churn, retention, contractual settings, access services, hidden Markov models, RFM, latent variable models

Suggested Citation

Ascarza, Eva and Hardie, Bruce, A Joint Model of Usage and Churn in Contractual Settings (April 10, 20112). Available at SSRN: https://ssrn.com/abstract=1898552 or http://dx.doi.org/10.2139/ssrn.1898552

Eva Ascarza (Contact Author)

Harvard Business School ( email )

Soldiers Field
Boston, MA 02163
United States

HOME PAGE: http://evaascarza.com

Bruce Hardie

London Business School ( email )

Regent's Park
London, NW1 4SA
United Kingdom

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