Suppose I have a group of 100 counties. Further suppose that the state decides to allocate a lump sum amount of money to some counties each year to boost spending on education in that county (until, say, 50 of the 100 counties have received money). Suppose my goal is to use a dif-in-dif approach to analyze the effect of the spending increase.
How would I specify this DID regression? The basic idea is that, for each year, I want to compare educational outcomes in counties that receive increased funding with those that do not. I want to do this so that I eventually get to evaluate the effect for all 50 counties that receive this educational funding boost.
My guess is something like this: I need to specify a typical DID regression with year and county FE s.t. for any given year, a county that receives funding is in the treated group and any county without the funding boost is in the control group. However, the effect of that funding boost means that a county treated in year $t$ ought not be included in the control group in year $t+1$, despite not receiving a funding boost in $t+1$.
Am I over complicating this? It doesn't seem to me like specifying a normal DID with year and county FE will quite work.