nbreg DiD: pooled post-period AME outside range of year-specific AMEs from separate model specifications

[Shin Lee]

I am running a difference-in-differences analysis with a negative binomial model and report three sets of estimates: a Year 1 effect, a Year 2+ effect, and a separate pooled post-period effect from an independent regression. In several subgroups, the pooled estimate falls outside the range defined by the Year 1 and Year 2+ estimates. Is this expected behavior when the pooled and period-specific estimates come from separate model specifications with different treatment indicators? Are there published examples in the health policy literature where this pattern is documented or discussed?