Abstract
Firms target customers with the best response to a marketing intervention to maximize its effectiveness or ROI. Doing so requires firms to identify differences in customer sensitivity, estimates that they often obtain using uplift / heterogeneous response models (Wager and Athey 2018, Ascarza 2018, Lemmens and Gupta 2020). While those methods have been proven effective in several marketing contexts, such as customer retention, product adoption, and ad effectiveness, little is known about their performance when firms try to estimate the sensitivity of a long-term outcome, as is generally the case. In theory, the observation window should not alter the way firms optimize their resource allocation – i.e., to maximize the long-term customer value, they should target customers with the highest predicted treatment effects in the long run. However, long-term measures accumulate random behaviors over time in practice, which can cause systematic bias even though common causal assumptions hold. As a result, targeting customers based on predicted long-term lifts results in suboptimal policies.
We show two distinct estimation biases arise when estimating long-term treatment effects on repeated purchase measures. First, uplift models often misattribute random purchase behaviors to the intervention and observed covariates, leading to a systematic bias (commonly known as the collider bias) for customers with unexpectedly high (or low) purchase counts. Besides, typical regression setups fail to identify the actual response function when the outcome is a repeated purchase measure – the multiplication of lifetime and purchase frequency makes random shocks in each process interact with the mean function. In this case, uplift models that estimate long-term effects can systematically overfit random shocks if we do not consider churn and purchase frequency separately.
Building on literature in statistical surrogacy (Athey et al. 2019, Yang et al. 2022) and buy-till-you-die models (Schmittlein et al. 1987, Fader et al. 2005, Abe 2007), we propose an imputation approach that overcomes these biases and enables firms to increase the effectiveness of interventions in the long run. Our solution captures the carry-over effect of short-term behavior change and overcomes the identification problem by carefully separating the churn and transaction processes. Using simulation and a real-world experiment, we show that our approach can significantly reduce the estimation bias and improve the long-run targeting profit by 11 – 28%.