[Guest]

Exactly, that's what I mean. I'm confused now.
The following code you suggested [xtreg unemp i.treat i.post i.treatpost i.sex age, fe vce(cluster n_city)] does not account for fixed differences between cross-sections, does it?
As far as I know, when running panel regressions, I need to include a set of dummies to control for fixed differences between cities (city-fixed effect) and a set of dummies to control for trends that are common to all cities (year fixed effect)

That's why I put 'i.year' instead of 'i.post' in the regression and that gives different DD estimates.

The code in #2: xtreg unemp i.treat i.post i.treatpost i.sex age, fe vce(cluster n_city)
My code: xtreg unemp i.treat i.year i.treatpost i.sex age, fe vce(cluster n_city)

[Clyde Schechter]

You do not invariably need to include year effects in the model. If the nature of the outcome variable is such that substantial year to year shocks that apply across the board to all cities are expected, then you should include that. But otherwise they are unnecessary and can lead to overfitting the noise in the data. This is a modeling decision and it is made based on your theoretical understanding of the data generating process in the real world.