I have a high-frequency panel dataset on the order of $i=150$ and $t=5000$. I am interested in studying the causal impact of a treatment with the following characteristics:
- The same unit can be treated several times
- Different units can be treated at different times
- The effect of the treatment does not spill over beyond the current time period
Here is an example of treatment over time (where black indicates treated, and the y axis contains a row for each unit $i$):
Here is an example of a treated unit (black) and a comparison unit (blue) when treatment is administered (red), where the $y$ axis is an outcome of interest:
Coming from the perspective of causal inference / program evaluation, it seems like the natural approach is to use some sort of difference-in-differences flavored model, where treated units act as controls for untreated units at different points in time. However, I am struggling to find an analogy in the literature.
- Typically, in example diff-and-diff models I have seen, units are treated only once, control units are never treated, and the treatment persists into the future.
- Also, with such a long time horizon autocorrelation seems problematic, and time-varying, individual-level seasonal fixed effects are likely necessary. Consequently, I expect that I need to make some modifications to the basic panel approach of including fixed effects for $i$ and $t$.
My question is:
- Have people used diff-in-diff analyses with similar datasets? If so, could you point me to some sample papers?
- Is there an alternative approach that would be be better suited to this setting? If so, are there relevant references? (e.g. from macro, finance, time series literature).
Thanks for any guidance you can provide.