[notahacker]

tldr; it doesn't, but offline vendors that collect your contact information they can anonymously check the proportion of purchasers which might [incidentally?] have been shown their ad on Facebook's network. Only a media buyer with a budget bigger than their brain would assume causality.

[jessriedel]

Couldn't Facebook easily demonstrate causality by running an RCT? Just randomly select half of a certain demographic to show the ad to, and then show that those users are more likely to make a purchase later.

[notahacker]

Theoretically yes, but I think with standard Facebook ad units and regular consumer brands sold in stores they'd be pretty unhappy with the results...

(since probability of giving stores your contact details post purchase and susceptibility to marketing messages pre-purchase are probably positively correlated and Facebook is permanently running concurrent trials of different kinds and being very selective about what they share, any positive effect they did manage to identify should be viewed as an almost certain overstatement of the ads' actual effectiveness anyway)