I am estimating a standard two period difference in differences model, where I estimate whether a policy change was associated with an individual level behavior change in a state that implemented it in comparison to the neighboring states that did not implement it. As controls, I am using neighboring states that appear to have had a parallel trend in the behavior prior to the policy change.
As my next step, I would like to evaluate how the policy change might have impacted the behavior of different subgroups within the treated state. For example, wealthier people might have changed their behavior less than poor people. I plan to do this by stratifying my analyses.
My question is: When evaluating subgroup effects, do I need to re-consider whether the pre-treatment trends were parallel in the treated states and the potential control states for each subgroup?
This could potentially lead to having a different set of control states for the overall population analysis and for the subgroup analysis because the overall parallel trend need not mean that the subgroup trend is parallel as well.