Modelling Customer Lifetime Value under Endogenous Marketing Interventions: A Structural Bayesian Approach

Abstract

Customer lifetime value (CLV) is the present value of future profits from customer relationships and serves as a fundamental metric for resource allocation in modern marketing. Extant probabilistic approaches—notably the Pareto/NBD and BG/NBD models—estimate CLV from observed purchase histories but often overstate marketing effectiveness by treating marketing interventions as exogenous. In practice, however, firms allocate marketing strategically, targeting customers based on observable and unobservable characteristics that also predict purchase behavior, thereby inducing endogeneity. We develop a structural Bayesian framework that jointly models (i) the customer purchase process as a function of latent autonomous propensity and marketing responsiveness, and (ii) the firm’s marketing assignment process as a function of observable customer attributes and estimated response signals. By integrating causal inference principles with hierarchical Bayesian modeling, the proposed framework mitigates bias arising from endogenous marketing assignment and enables more reliable estimation of marketing effects on CLV. Monte Carlo simulations calibrated to retail e-commerce settings show that conventional CLV models can overestimate marketing elasticity by 20–40%, with bias increasing in targeting sophistication. The proposed approach recovers more accurate heterogeneous treatment effects, supporting improved customer segmentation and more effective budget allocation. Methodologically, this research extends causal inference to the lifetime value setting; substantively, it quantifies and corrects a key source of bias in contemporary CLV practice