Justin Whitehouse, William Betz, Yan Zhang, Peter Coles, Ramesh Johari, Vasilis Syrgkanis
arXiv 6 Oct 2026 · Econometrics
arXiv:2610.08558 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Norvell, Tim and Horky, Alisha (2017) Gift card program incrementality and cannibalization: the effect on revenue and profit | 1.000 | 5 | 3 | 100% |
| 2 | Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Du… (2018) Double/debiased machine learning for treatment and structural parameters | 0.928 | 4 | 3 | 100% |
| 3 | Athey, Susan and Chetty, Raj and Imbens, Guido W and Kang, Hyunseung (2025) The surrogate index: Combining short-term proxies to estimate long-term treatment effects more rapidly and precisely | 0.644 | 3 | 2 | 67% |
| 4 | Prelec, Drazen and Loewenstein, George (1998) The red and the black: Mental accounting of savings and debt | 0.644 | 2 | 2 | 100% |
| 5 | Thaler, Richard (1985) Mental accounting and consumer choice | 0.644 | 2 | 2 | 100% |
| 6 | Van Der Laan, Mark J and Rubin, Daniel (2006) Targeted maximum likelihood learning | 0.644 | 2 | 2 | 100% |
| 7 | White, Rebecca J (2006) Format matters in the mental accounting of funds: The case of gift cards and cash gifts | 0.644 | 2 | 2 | 100% |
| 8 | Chernozhukov, Victor and Newey, Michael and Newey, Whitney K and Sin… (2023) Automatic debiased machine learning for covariate shifts self | 0.606 | 6 | 2 | 33% |
| 9 | Prentice, Ross L (1989) Surrogate endpoints in clinical trials: definition and operational criteria | 0.511 | 3 | 2 | 33% |
| 10 | Van der Vaart, Aad W (2000) Asymptotic statistics | 0.511 | 3 | 2 | 33% |
Showing the top 10 of 72 scored citations.