Robust Causal Inference for Incremental Return on Ad Spend with Randomized Geo Experiments

Evaluating the incremental return on ad spend (iROAS) of a prospective online marketing strategy---that is, the ratio of the strategy's causal effect on some response metric of interest relative to its causal effect on the ad spend---has become progressively more important as advertisers increasingly seek to better understand the impact of their marketing decisions. Although randomized "geo experiments" are frequently employed for this evaluation, obtaining reliable estimates of the iROAS can be challenging as oftentimes only a small number of highly heterogeneous units are used. In this paper, we formulate a novel statistical framework for inferring the iROAS of online advertising in a randomized paired geo experiment design which further motivates and provides new insights into Rosenbaum's arguments on instrumental variables, and we propose and develop a robust and distribution-free estimator "Trimmed Match" which adaptively trims poorly matched pairs. Using numerical simulations and real case studies, we show that Trimmed Match can be more efficient than some alternatives, and we investigate the sensitivity of the estimator to some violations of its assumptions. Consistency and asymptotic normality are also established for a fixed trim rate. Technical proofs are provided in the appendix.