  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
\citep{chan2017,wolfe2016}.
  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 \textit{back-door} criterion
\citep{pearl2013causality}. 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.
