A generalized framework for estimating customer lifetime value when customer lifetimes are not observed

Measuring customer lifetime value (CLV) in contexts where customer defections are not observed, i.e. noncontractual contexts, has been very challenging for firms. This paper proposes a flexible Markov Chain Monte Carlo (MCMC) based data augmentation framework for forecasting lifetimes and estimating customer lifetime value (CLV) in such contexts. The framework can be used to estimate many different types of CLV models---both existing and new. Models proposed so far for estimating CLV in noncontractual contexts have built-in stringent assumptions with respect to the underlying customer lifetime and purchase behavior. For example, two existing state-of-the-art models for lifetime value estimation in a noncontractual context are the Pareto/NBD and the BG/NBD models. Both of these models are based on fixed underlying assumptions about drivers of CLV that cannot be changed even in situations where the firm believes that these assumptions are violated. The proposed simulation framework not being a model but an estimation framework allows the user to use any of the commonly available statistical distributions for the drivers of CLV, and thus the multitude of models that can be estimated using the proposed framework (the Pareto/NBD and the BG/NBD models included) is limited only by the availability of statistical distributions. In addition, the proposed framework allows users to incorporate covariates and correlations across all the drivers of CLV in estimating lifetime values of customers.