In general, selection bias results in over-estimating the effectiveness of ads because ads are shown to those most likely to buy, e.g., as advertisers employ techniques like machine learning to maximize the effectiveness of ad campaigns.
However, a new study from facebook finds a way to cleverly construct a control group that is not subject selection bias. By comparing "conversion" rates for the winner of an ad auction, e.g., page viewing, registering, or buying, to what would have happened had the second-best bidder won the ad auction, facebook estimates the causal effect of ads (free from selection bias).
Because facebook has "single user login" they can:
- make sure that no one in the control group has seen the ad; and
- track conversions across different devices and for several weeks after ad exposure by embedding a "conversion pixel" on the checkout confirmation page.
The study concludes that targeted ads a 73% increased likelihood of conversion.
UPDATE FROM READER: I think that this is the same idea as "ghost ads". See simple exposition or the paper.(Ungated: https://courses.cit.cornell.edu/jl2545/adpapers/Randall%20Lewis.pdf)