Colinearity Problem with Policy Dummy & Time Trend

[Dirius]

Dear all,

I have a pooled cross section with annual data and I am analysing the effects of a policy intervetion. To do this I included a dummy variable for all years after the year in which the treatment took place. Additionally I would like to include time dummies to account for general trends. Is that possible? I constantly get "Near singular matrix". I do not believe that this is the dummy trap and I have tried a nonlinear "fading-out" for my treatment dummy (i.e. a high value forv the year in which the treatment happened and a gradual decrease for the years afterwards), without success.
I am also accounting for country-specific fixed effects but removing that also does not change the problem.

I would be grateful for a hint.