I did come to realize that when controlling for time effects and region effects in a regular regression, it is pretty normal and understandable to use the prefix .i for both time and region variables.

For example, reg y x i.year i.region, cluster(region)

However, when the interaction is also required, there are some posts around here and other sites suggesting the use of the prefix c. for the time variable instead of the i. prefix.

For example, reg y x c.year##i.region, cluster(region)

Of course, the use of i.year##i.region will control for a) year fixed effects, b) region specific effects, and c) effects happening each year in each region. However, the use of c.year##i.region seems to be multiplying the dummy variables for each region by the year variable. The latter would suggest it is a sort of region-trend control variable.


QUESTIONS:
  1. Is my understanding correct?
  2. Is the use of either c. or i. contingent on what one wants to estimate?
  3. What is the best way to proceed in a difference-in-difference estimation? In particular, in a diff-in-diff approach with a staggered rollout at the region-year level.