I partly work in this space, and I can confirm that geo-fencing over a time period is the probably the most transparent and convincing (to the client) way to do this. Essentially you mark out local regions (as small as zip codes or as large as states, or something else in this spectrum), and ensure that your advertisements only show within certain "fences". And then you compare old and new numbers within those fences.
The technical aspect aside, there are a lot of "soft" factors that help: regular communication of easily consumable numbers/graphs/metrics to the client, calling out inconsistencies, etc. In other words, this is far from a fire-and-forget exercise; this can be an intense monitoring and client-engagement exercise.
The regular client engagement sometimes helps you in pinpointing cause-effect in the observations too. For ex company X might decide to advertise less of product Y in a certain state Z because of new laws there. But the team you're interacting with might not be aware of this change, or might not be cognizant of its potential impact on an advt. campaign. Regular dialogue helps here since you might observe a change in sales trends, and bring it up in a meeting - and the client team might be able to then rationalize the change. This is healthy for both parties.
The technical aspect aside, there are a lot of "soft" factors that help: regular communication of easily consumable numbers/graphs/metrics to the client, calling out inconsistencies, etc. In other words, this is far from a fire-and-forget exercise; this can be an intense monitoring and client-engagement exercise.
The regular client engagement sometimes helps you in pinpointing cause-effect in the observations too. For ex company X might decide to advertise less of product Y in a certain state Z because of new laws there. But the team you're interacting with might not be aware of this change, or might not be cognizant of its potential impact on an advt. campaign. Regular dialogue helps here since you might observe a change in sales trends, and bring it up in a meeting - and the client team might be able to then rationalize the change. This is healthy for both parties.