International Journal of Engineering and Management Research

Such bias propagates through CLV calculations, distorting customer valuation, segmentation, and budget allocation decisions (Ali and Shabn, 2024).

This paper makes three contributions. First, we formalize the identification challenge arising from endogenous marketing assignment in CLV models, showing how strategic targeting induces correlation between marketing exposure and unobserved determinants of purchase behavior. Second, we develop a structural Bayesian framework that jointly models customer purchase behavior and firm marketing assignment decisions, thereby improving identification of causal marketing effects in the presence of selection bias. Third, using Monte Carlo simulations, we demonstrate that accounting for endogenous marketing substantially alters CLV estimates and customer rankings, with meaningful implications for targeting and resource allocation. By integrating insights from causal inference with hierarchical probabilistic modelling, the proposed framework advances both the methodological and practical understanding of CLV estimation.

2. Literature Review

2.1 Traditional and Probabilistic Customer Lifetime Value Models

The contemporary study of customer lifetime value originated with foundational conceptual work by Shaw and Stone (1988) establishing CLV as a metric for evaluating long-term customer profitability in database marketing contexts. Early implementations employed deterministic calculations of discounted future cash flows, but these approaches proved inadequate for non-contractual settings wherein the precise timing of customer defection remains unobserved.

The field advanced substantively with the introduction of probabilistic frameworks designed for non-contractual purchase environments. Schmittlein et al. (1987) proposed the Pareto/NBD model, which specifies that customer purchase behavior follows a Poisson process with heterogeneous purchase rates distributed via gamma distribution, while customer attrition (silent churn) follows an exponential distribution parameterized through a Pareto distribution across the customer base.

Pioneering applications (Erdem & Keane, 1996) demonstrated that hierarchical Bayes estimation substantially improves prediction, particularly for customers with sparse transaction histories, by inducing shrinkage of individual-level estimates toward population means.

The hierarchical Bayesian framework exhibits particular utility in accommodating observed covariates that vary across customers. By permitting population-level hyperparameters to depend upon observable customer characteristics, the framework enables parameter heterogeneity to correlate systematically with customer attributes (e.g., acquisition channel, geographic location, demographic segment). This structure proves natural for CLV modeling wherein customer purchase propensity manifestly varies with observable characteristics.

Nevertheless, even sophisticated hierarchical Bayesian CLV models maintain silence regarding the causal impact of marketing interventions. They continue to treat marketing assignment as exogenous, thereby failing to address the fundamental problem that firm targeting decisions induce correlation between marketing exposure and unobserved customer characteristics that simultaneously predict purchase behavior. This limitation reflects a gap between the models' formal specification (as purely customer demand-side processes) and actual firm practice (wherein marketing assignment reflects managerial expectations about customer responsiveness).

2.3 Endogeneity in Marketing and Causal Inference

The marketing econometrics literature has extensively developed methodology for addressing endogeneity in specific domains—price setting, promotional elasticity, advertising response—yet has not systematically applied these techniques to the CLV setting. Chintagunta et al. (2006) provide a comprehensive taxonomy of endogeneity sources applicable to marketing: omitted variables (unobserved factors affecting both treatment and outcome), simultaneity (bidirectional causality between treatment and outcome), measurement error, and selection bias (non-random assignment to treatment). Selection bias—wherein treatment receipt is correlated with unobserved factors predicting outcomes—constitutes the primary threat in CLV estimation contexts.

We integrate structural econometric approaches—specifically, joint modeling of customer purchase behavior and firm marketing strategy—with hierarchical Bayesian estimation to recover more reliable estimates of causal marketing effects on long-term customer value. To our knowledge, existing literature does not jointly model customer purchase behavior and firm marketing assignment decision-making within a unified framework designed to estimate causal effects on customer lifetime value.

3. Conceptual Framework

Formal identification of causal marketing effects requires careful modeling of two distinct behavioral processes: (i) customer purchase behavior as a function of intrinsic propensity and marketing exposure, and (ii) firm targeting behavior as a function of observed customer characteristics and estimated propensity. We next articulate the economic logic underlying each process and the identification challenge arising from their interaction.

3.1 Customer Decision Process

We conceptualize customer purchase behavior as determined by two latent factors: (i) an autonomous purchase rate λᵢ reflecting the customer's intrinsic propensity to engage with the firm (driven by category need, brand affinity, and competitive alternatives), and (ii) a marketing elasticity coefficient mᵢ reflecting the customer's estimated responsiveness to firm-directed marketing stimuli. The purchase probability in period t for customer i, conditional upon remaining active (i.e., not yet churned), depends upon both factors in additive form within a linear probability framework: autonomous propensity provides a baseline purchase inclination, while marketing exposure incrementally increases purchase probability by an amount proportional to the customer's elasticity.

Both λᵢ and mᵢ remain unobserved by the analyst; their values must be inferred from observed purchase histories using Bayesian procedures. Unobserved heterogeneity in these parameters across the customer base reflecting the manifest fact that customers differ in intrinsic purchase propensity and response to marketing constitutes an essential feature of the model. Additionally, customer attrition (the silent defection characteristic

3.3 The Endogeneity Mechanism and Resulting Bias

The observed correlation between marketing exposure and purchase outcomes conflates two distinct causal flows. First, there is the direct causal impact of marketing on customer purchases (the "treatment effect" of interest). Second, there is selection bias: high-propensity customers are preferentially targeted, so observed purchase differences reflect both causal marketing effects and the concentration of marketing on customers naturally disposed toward purchase.

Consider a concrete illustration. A firm observes that customers in the top quintile of past purchase frequency receive 50% of the email budget and achieve 2.5× higher purchase rates than customers in the bottom quintile who receive 5% of the email budget. A naive analyst might estimate that email marketing increases purchase probability by 250%. However, if the firm's targeting criteria (past purchase frequency) strongly predict autonomous purchase propensity λᵢ—customers with high past purchase frequency are intrinsically high-propensity customers—then much of the 2.5× difference reflects selection, not causality. The firm may be spending email budget on customers who would purchase anyway, reducing the true causal elasticity of email.

Correcting this bias requires joint modeling. By explicitly specifying how the firm's targeting decisions depend upon customer characteristics and propensity factors, and by leveraging the structure of customer purchase histories, we can construct predictions of what targeting would have occurred under alternative firm decision-making rules. This counterfactual reasoning enables statistical adjustment for selection bias and recovery of causal effects. The key identifying assumption is that customer purchase history (frequency, recency, timing patterns) predicts latent propensity λᵢ and elasticity mᵢ, but conditional on observable targeting rules (e.g., RFM-based segmentation), residual variation in purchase timing does not directly influence future marketing assignment beyond what is captured by the firm's implemented targeting criteria.

Customer heterogeneity in propensity and elasticity is accommodated through hierarchical prior distributions, permitting parameters to vary across customers while enabling information pooling. Specifically:

Weakly informative priors are specified on the hyperparameters to allow the data to drive inference while preventing overfitting.

The hyperparameters μ_λ, σ_λ, μ_m, σ_m characterize the population-level distribution of customer preferences and treatment effects. By estimating these hyperparameters from data rather than imposing them a priori, the model learns the cross-customer variation in purchase propensity and marketing responsiveness. This hierarchical structure ensures that customer-level parameter estimates—particularly those based upon limited transaction histories—are shrunk toward the population mean, improving prediction by exploiting correlations in customer behavior.

The critical innovation relative to extant CLV models is the explicit inclusion of the marketing exposure term mᵢ · Zᵢₜ in the purchase equation. Standard probabilistic CLV models (Pareto/NBD, BG/NBD) omit marketing entirely, leaving marketing effects to be absorbed into unobserved heterogeneity. By explicitly modelling marketing, we enable direct estimation of the treatment effect mᵢ and allow assessment and correction of endogeneity bias through the targeting module.

The likelihood is constructed from conditional purchase probabilities across customers and time periods.

Customer attrition is modelled through a separate binary indicator Active_it ∈{0,1}, which transitions from 1 to 0 upon silent defection. The attrition process depends upon customer-specific factors (autonomous churn propensity) that are independent of marketing activity, reflecting that customers defect through mechanisms—competitive switching, category exit—outside firm control.

4.3 Identification and Bayesian Inference

Identification of causal marketing effects is facilitated by the structure of the assignment module combined with the temporal sequence of firmdecisions and customer outcomes. Identification is achieved through the joint specification of the demand and assignment processes within a hierarchical Bayesian framework, rather than relying on a strict instrumental variable.

The firm makes targeting decisions Z_i based upon information known at the time of targeting (observable characteristics and signals of propensity estimated from historical data). Customer purchases occur subsequently. Conditional upon the observable criteria X_i that explicitly appear in the firm's targeting rule—and are therefore known to be used by the firm—the randomness in purchase timing contains information about latent propensity and elasticity that is not fully captured by the firm's targeting mechanism, helping to separate selection effects from marketing impact.

Bayesian inference proceeds via Markov Chain Monte Carlo (MCMC) estimation. The hierarchical structure yields conjugate conditional posterior distributions for some parameters, enabling efficient Gibbs sampling within blocks (e.g., individual and conditional upon hyperparameters). Non-conjugate blocks (e.g., hyperparameters μ_λ, σ_λ, μ_m, σ_m) are estimated via Metropolis-Hastings sampling with adaptive proposals. Model specification includes weakly informative priors on hyperparameters—normal priors with large variances on means, half-normal priors on standard deviations—to avoid overfitting, allowing data to dominate inference.

Posterior inference enables two key outputs. First, posterior means and credible intervals for individual customer parameters (λᵢ, mᵢ)quantify heterogeneous propensities and treatment effects, enabling customer-level segmentation based on estimated marketing responsiveness. Second, posterior predictive distributions enable counterfactual CLV calculations: the analyst can sample from the posterior distribution, set marketing exposure to alternative levels (e.g., zero for all customers, or optimized targeting rules), and draw samples of resulting future purchases. Averaging these counterfactual purchase samples yields posterior predictive CLV distributions under alternative marketing scenarios, supporting robust decision-making under uncertainty.

Second, the corrected model enables superior budget allocation. Traditional CLV frameworks suggest concentrating marketing on customers with high autonomous purchase propensity (who will likely buy anyway). The corrected framework instead directs marketing toward customers with high elasticity those for whom marketing is most effective in a causal interpretation sense under the model even if their autonomous propensity is modest. This reallocation of marketing budgets from high-propensity/low-elasticity segments to low-propensity/high-elasticity segments can substantially increase firm profitability.

Third, the framework enables valid scenario analysis. Marketing managers frequently contemplate counterfactual allocations: "How would CLV change if we reduced email frequency by 20%?" or "What additional CLV would we realize by shifting budget from digital to direct mail?" Valid answers require well-identified estimates of marketing effects. Our framework provides posterior predictive distributions of CLV under alternative marketing regimes, enabling probabilistic scenario analysis. Decision-makers can quantify not only point estimates of CLV under alternative strategies but also credible intervals reflecting estimation uncertainty.

6. Simulation Evidence

To validate the magnitude of endogeneity bias and the efficacy of our proposed correction, we conduct Monte Carlo simulation studies calibrated to approximate realistic e-commerce retail environments. We generate synthetic customer purchase and marketing exposure data from a known data-generating process, then estimate both standard CLV models (ignoring marketing) and our proposed structural Bayesian model (jointly modelling purchase and targeting), comparing recovered parameter estimates to ground truth.

We develop a structural Bayesian framework jointly modeling customer purchase decisions and firm marketing allocation decisions, enabling improved identification and estimation of marketing effects on long-term customer value.

The research makes contributions across three dimensions. Methodologically, it extends causal inference techniques from point-in-time treatment effects to the lifetime value setting, where outcomes accumulate over time. Theoretically, it bridges previously separate literatures (CLV modeling and marketing econometrics) and demonstrates how insights from causal inference improve foundational customer analytics models. Practically, it enables firms to more accurately assess which customers are valuable, direct marketing expenditures toward customers exhibiting higher estimated responsiveness, and conduct scenario analysis of alternative marketing strategies.

Promising directions for future research include: (1) relaxing the linear utility specification to accommodate nonlinear marketing response and saturation effects characteristic of high-frequency marketing; (2) modeling the firm's optimization problem to derive endogenous optimal targeting policies rather than treating targeting as exogenously specified; (3) extending the framework to multiproduct settings with competitive brand choice; (4) incorporating dynamic customer information states wherein the firm's propensity estimates improve over time; and (5) empirical validation using customer databases with measured marketing exposure and complete transaction records.

The proposed framework relies on assumptions regarding the firm's targeting process and model specification; deviations from these assumptions may affect the accuracy of estimated effects.

The central insight that marketing endogeneity creates substantial bias in CLV estimates and that joint modeling of customer behavior and firm strategy can mitigate this bias—will become increasingly important as firms develop more sophisticated ML-driven targeting algorithms, making the endogeneity problem more acute rather than less.

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