Hi KireFdz,
I met a similar problem regarding negative log inputs couple of days befroe. I try to partially answer it.
The following resource is useful:
Pfeifer (2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”
or you can find it at https://www.dynare.org/resources/
The general answers are located among Section 4.2 to Section 4.5 (Page 48). Especially read Footnote 25 and Remark 19. In words, if the variables can be zero or negative, we do not put them into \exp(), instead just write what you see into the model; section.
Overall, there will be a mixing format of both log-linearization for positve variables and linearization for other variables in your dynare model.
If my explanation was wrong, please kindly let me know. Thank you in advance! 