Steady_state_model block two sector NK

Dear all

I am working on a two sector NK model similar to this one by Chang et al 2021 (https://onlinelibrary.wiley.com/doi/full/10.1111/jmcb.12775). Even though I am an experienced dynare user, this is the first time I struggle so much to find a steady state. The model is big, however I was able to derive analytical solutions by hand following the method of a previous working version of the same paper (see here: https://www.imf.org/en/Publications/WP/Issues/2019/06/10/Fiscal-Consolidation-and-Public-Wages-46913). Note that I use a simpliefied version of this and at this stage I care only about the steady state

In order to exploit the analytical solutions of the model I use the steady_state_model feature, but I cannot get a solution no matter what. I see some small residuals in two/three equation but overall the analytical solutions seem to satisfy the equations of the model

Note that when I use the definitions of the steady_state_model block in a separate external m-file I can get, recursively, values for my variables which I would say are all plausible. In other words the analytical solutions give something meaningful. But they are useless when I use them in the model.

So my questions are:
1/ Does this mean that there is something wrong in the way the model is structured? Maybe a theoretical mistake
2/ Is there any other computational hint to calculate steady state or anyother check to test what is going wrong?

I would appreciate your thoughts. I attach the mod (a bit messy but runs).

cypgem2sec_SS_noG4.mod (14.3 KB)
external.m (4.4 KB)

best
Stelios

I spot two equations with residuals in the range of 0.3 (which incidentally seem to be linked). I would focus on those. Alternatively, you may opt for a more radical strategy of fixing some variables like labor and then adjusting the parameters accordingly. That is often simpler.