It's unclear how this experiment would be done. In the case of brand advertising, it's likely that brand awareness would decay over some period of time and in turn purchase behavior would change.
It's not currently possible to run an A/B experiment with a hold out group of potential customers across all channels, let alone for any longer duration experiment. So how can we separate cause and effect? (although pay per conversion channels do get gamed left and right)
Come up with some new product that requires some personal data for usage (eg. age, gender/sex, address). Start to advertise this in just one country to one demographics, and look how many out-of-target orders you get.
Maybe it's even enough if you simply just sell it via mail order, you can then look at the addresses.
There's probably a natural information spread in any market (word of mouth, trade magazines), and there's probably a physical dispersion of the target group of people too (people move, visitors/tourists saw the ad/product and order it at home), but it still should be a valuable to see how much effect just one campaign has.
Maybe one of the best products for this could be a car. They are pretty standard, really not much difference between them, they are in all price ranges, and regularly new models come out. Advertise one in a few major US cities but don't in others.
For most vendors, not possible to accurately target age/sex/address online. They will certainly sell you the option, but they won't tell you how accurate the data is - or they will provide it a high accuracy with extremely low coverage.
To see this in action - spend a day watching pitbull videos on youtube and see how many spanish language ads you'll get.
Traditional brand advertising testing (TV, newspaper, etc.) would be geography segmented as I understand it. So half the cities got the campaign and half didn't. You can mimic that with IP based geo-location although you'd get more leakage than pre-internet.
It's not currently possible to run an A/B experiment with a hold out group of potential customers across all channels, let alone for any longer duration experiment. So how can we separate cause and effect? (although pay per conversion channels do get gamed left and right)