Evaluating the return on ad spend (ROAS), the causal effect of advertising on sales, is critical to advertisers for understanding the performance of their existing marketing strategy as well as how to improve and optimize it. Media Mix Modeling (MMM) has been used as a convenient analytical tool to address the problem using observational data. However it is well recognized that MMM suffers from various fundamental challenges: data collection, model specification and selection bias due to ad targeting, among others (Chan & Perry 2017; Wolfe 2016).
In this paper, we study the challenge associated with measuring the impact of search ads in MMM, namely the selection bias due to ad targeting. Using causal diagrams of the search ad environment, we derive a statistically principled method for bias correction based on the back-door criterion (Pearl 2013). We use case studies to show that the method provides promising results by comparison with results from randomized experiments. We also report a more complex case study where the advertiser had spent on more than a dozen media channels but results from a randomized experiment are not available. Both our theory and empirical studies suggest that in some common, practical scenarios, one may be able to obtain an approximately unbiased estimate of search ad ROAS.