Third-Party Gift Cards Show Higher Incrementality

Gift-card programs create a measurement problem that ordinary transaction analysis cannot solve. A firm observes a card when it is redeemed in a purchase, but cannot see whether non-purchasers held an unredeemed card; comparing redeemers with everyone else therefore confounds treatment with customers’ pre-existing likelihood of booking. The paper develops a causal data-fusion estimator for this censored-treatment setting and applies it to Airbnb gift cards distributed through first-party, retail online, retail in-store, and B2B channels.

Core Contribution

The paper’s central contribution is an identification result for incremental revenue when treatment receipt is only partially observed in a large observational dataset. Let $G$ denote gift-card receipt, $B$ a booking decision, and $Y$ spend. The observational data reveal $S=B\cdot G$, rather than $G$ itself: a gift card becomes visible only when the customer books with it. This is more restrictive than conventional missing-data settings, because treatment status is systematically absent for the customers whose counterfactual behavior matters most.

The authors fill that gap with a smaller experiment in which treatment status is fully recorded. Their key assumption is not that the experimental and observational populations have identical booking probabilities. Instead, conditional on covariates, the ratio of ungifted to gifted booking probabilities must transfer between populations. That weaker invariance condition permits overall booking rates to differ by time, geography, or customer mix, provided the differences affect both treatment states proportionally.

Technical Approach

The estimator combines three learned nuisance components: an experimental ungifted booking probability, an experimental gifted booking probability, and observational organic spend among customers who book without a gift card. These terms reconstruct the counterfactual spend that observed gift-card purchasers would have generated without the program. The identification formula consequently separates the program’s effect on spend conditional on booking from its effect on whether a customer books at all.

For estimation, the paper derives Neyman-orthogonal moments and uses cross-fitting, so first-order error in the learned nuisance models does not dominate the target estimate. The Airbnb implementation estimates channels and months separately, uses five folds, fits experimental propensity models with LogisticRegression, and selects observational nuisance models with FLAML AutoML. The observational samples are large: monthly subsamples in 2024 range from 6,014,422 to 6,972,099 customers, while the experimental dataset has roughly 26,000 observations.

This is a useful distinction from simply applying an experiment-wide average treatment effect. The experiment can identify an effect for its own population, but the fused estimator uses the observational distribution to estimate incrementality where the business actually deploys cards. The price is that validity rests on transferability and covariate coverage rather than randomization alone.

Results and Analysis

The channel estimates make the difference between causal adjustment and naïve comparisons concrete. For the incrementality ratio, the proposed annual estimates are -0.119 for First-Party, 0.204 for Retail Online, -0.049 for Retail In-store, and 0.221 for B2B. Only B2B has a reported 95% interval excluding zero: 0.059 to 0.405. Retail Online’s interval, -0.006 to 0.415, is close to but still crosses zero. The paper’s directional conclusion that third-party channels are more incremental is therefore strongest for B2B; the Retail Online point estimate is consistent with the claim but not conclusive at the reported interval.

The contrast with unadjusted observational estimates is substantial. A memoryless unadjusted fusion estimate ranges from 0.383 to 0.441 across channels, while simple observational intensive-margin estimates range from 0.251 to 0.324. Those estimates are much larger than the proposed ratios, which supports the paper’s warning that redeemer-versus-non-redeemer comparisons attribute selection effects to the program. The experiment-only estimate across all channels is 0.076 with a 95% interval of -0.010 to 0.163, indicating that the small experiment alone lacks precision for channel-level conclusions.

The self-gifter analysis adds a commercially relevant but less cleanly identified segmentation result. Using redemption within one week of purchase as a proxy, suspected self-gifters account for mean shares from 11.6% in First-Party to 51.0% in B2B. Their estimated incrementality ratios range from 0.342 in B2B to 0.504 in Retail In-store, and the authors report higher ratios than in the full population. That pattern is plausible if self-gifters use discounts to make trips that would otherwise not occur, but it remains dependent on a behavioral proxy rather than observed intent.

Limits for Deployment

The method estimates incrementality, not profitability. Distribution discounts, third-party fees, fraud-monitoring costs, and card breakage can differ sharply by channel, so a positive incrementality ratio does not establish that a channel earns money. More fundamentally, the causal result depends on the conditional risk-ratio transferability assumption. The experiment notified recipients by email and was conducted in 2022, whereas the observational data are from 2024; the paper addresses resulting mode and temporal differences with features and sensitivity analyses, but cannot directly verify invariance. The evidence is strongest as a disciplined measurement framework for similar businesses with a relevant experiment, not as a channel-ranking rule that transfers unchanged across firms.