A Joint Model of Usage and Churn in Contractual Settings

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 multiperiod forecasts of customer behavior. Although 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 developing 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 on different time scales (or “clocks”), 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 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 useful 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).