Measuring Gift Card Program Incrementality via Causal Data Fusion

2026-10-06

AI Summary

This study addresses the challenge of accurately estimating the causal effect on incremental revenue when gift card holding status is censored in observational data. To overcome this information deficiency, we propose a novel data fusion framework that integrates large-scale observational data with small-scale experimental data under a transportability assumption. Furthermore, we construct a flexible machine learning-based estimator and rigorously establish its asymptotic normality. Applying this methodology to Airbnb’s channel analysis, our empirical findings reveal that third-party channels and self-gifting users exhibit significantly higher incremental effects. Ultimately, this work provides a solution for causal inference in complex censoring scenarios that offers both theoretical guarantees and practical utility.

Abstract

Businesses regularly offer gift card programs to drive customer spending and increase engagement. A central question is how much incremental revenue these programs generate, and which channels drive it most efficiently. Measuring the incremental revenue associated with a gift card program is a challenging problem in causal inference, requiring a firm to infer how much each customer would have spent if they never received a gift card. Observational data on past customer purchasing behavior reveal possession of a gift card only when a customer makes a purchase, thus leaving a customer's treatment status systematically censored. In this paper, we develop a novel data fusion approach to overcome this missing data challenge. We identify and estimate incrementality by combining a large observational dataset with a smaller experimental dataset from a different population. Our approach relies on a mild transferability condition, which posits that the conditional relative treatment effect of gift card receipt on the decision to purchase is invariant across the two populations. We develop a flexible, machine learning-based estimator for the incremental revenue and establish its asymptotic normality. We apply our estimator across both first- and third-party channels through which Airbnb distributes gift cards, finding heterogeneity in incrementality across segments of the population. In particular, we find not only that third-party channels are more incremental than first-party ones, but also that "self-gifters" (i.e., customers likely to have purchased their own gift cards) are more incremental than the broader population.

Problem

• incrementality
• causal inference
• gift card program
• missing data
• observational censoring

Innovation

• Causal Data Fusion
• Incrementality Estimation
• Transferability Assumption
• Machine Learning Estimator
• Missing Data