Online Causal Inference for Advertising in Real-Time Bidding Auctions

Real-time bidding systems, which utilize auctions to allocate user impressions to competing advertisers, continue to enjoy success in digital advertising. Assessing the effectiveness of such advertising remains a challenge in research and practice. This paper proposes a new approach to perform causal inference on advertising bought through such mechanisms. Leveraging the economic structure of first-and second-price auctions, we establish novel results that show how the effects of advertising are connected to and, hence, identified from optimal bids. Importantly, we also outline the precise conditions under which these relationships hold. Because these optimal bids are required to estimate the effects of advertising, we present an adapted Thompson Sampling algorithm to solve a multiarmed bandit problem that succeeds in recovering such bids and, consequently, the effects of advertising, while minimizing the costs of experimentation. We also show that a greedy variant of this algorithm can perform just as well, if not better, when exploiting the structure of the model we consider. We use data from real-time bidding auctions to show that it outperforms commonly used methods to estimate the effects of advertising.