I have panel data of sales for many stores in two comparable cities. One of the cities holds a special event once a month (the treatment) which is expected to boost sales across the board on that day. I would like to estimate the average treatment effect on the treated, i.e. identify whether or not the special event does what it should.
While the two cities are quite comparable (and I can find a number of controls for the stores), sampling is clearly not random. Furthermore, there is autocorrelation in sales between dates at each individual store, and it seems reasonable to think the monthly seasonality of the treatment has some impact.
My question is twofold.
1/ Do you think running a difference-in-differences analysis in this “experimental” setup makes sense at all?
2/ The examples of diff-in-diffs I have seen are all pre-treatment/post-treatment. Do you have any idea of how I could account for the periodicity of the treatment? It seems wrong to consider each month separately because of the autocorrelation.
Thank you very much for your help!