I'm evaluating the effect of a policy change on a count outcome across a number of units over time. I have panel data for 300 units over 20 time periods, with roughly 20% of units exposed to the policy change at different points in time. I want to include unexposed units in order to better control for time trends.
I'm using negative binomial regression and I'm unsure whether I need to include an offset term to account for the difference in length of time units are exposed to the policy change considering the fact that I have an observation for every time period after a unit is exposed (exposure length is the same at the observation level).
If I do need an offset, how do I specify this for time periods before exposure and for control units?