The Problem of Ignoring the Ignorability Assumption in Advertising Measurement: A Matrix Completion Solution

Digital platforms increasingly rely on algorithms for decision making. A canonical success story is online advertising, where platforms use algorithmic auctions to allocate ads efficiently and maximize revenue. Another pillar of these platforms’ long-term success is accurate causal measurement of advertising effectiveness. Although randomized experiments remain the gold standard, their high cost makes observational approaches appealing to both platforms and advertisers. In this paper, we show that the algorithmic nature of ad allocation fundamentally challenges causal measurement by violating the overlap assumption required for valid estimation. Even when treatment assignment is unconfounded, the deterministic structure of auctions implies that many users receive ads with near-zero or near-one probability, leading to biased estimates of ad effectiveness. We develop a novel framework that interprets this lack of overlap as a missing data problem and leverages variation across multiple advertising campaigns using matrix completion to recover causal estimates. Using both simulated and real advertising data, we demonstrate that our approach accurately recovers ad effects at aggregate and individual levels and substantially improves targeting efficiency, offering a scalable solution for causal advertising measurement in algorithmic markets. We conclude with a discussion of managerial implications and potential extensions to other algorithmic decision-making settings.

History: Olivier Toubia served as the senior editor.

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mksc.2023.0382.