I was thinking about running a diff-in-diff with fixed effect in order to deal with a panel data experiment. The problem is that I don't know how many datapoints I need in order to the experiment be reliable.
This is the thing: I want to see how my customers react to a change in price. An AB test doesn't look like a good alternative, due to cannibalization. So I would like to change the price of a bundle of products in some cities. Let's say for cities A, B, C and D, cleaning products will be 10% cheaper. Then I would run a diff-in-diff with fixed effects using each city datapoint. The question is: how many cities do I need in order to run this experiment? How many sales each city would have to have in order to the experiment be reliable?