Sorry, it might be, that I fundamentally misunderstand something here.

I took all the equations (before the log-linearization is done) from the paper I linked above, and I refer to them as the nonlinear model. So for example C_{rt}^{-1} = \beta R_t C_{rt+1}^{-1}\frac{1}{\Pi_{t+1}} for the Euler equation.

To calculate the steady-state, I replaced all endogenous variables, with their steady-state expression and removed the time subscript, so C_{rt} becomes \bar{C} for example. I refer to that as the steady-state model.

I now have 14 equations and 14 variables in my steady-state model. I substituted everything in the Phillips-Curve, until it only depended on inflation and since the equation became quite involved I used a numerical solver to solve for Pi. Given Pi, the rest of the equations in the steady-state model, could than be solved quite easily.

I than wrote a steady_state_model block (it’s in the Hansen2020_NotLinearized_Copy.mod from above), where I used a steady_state_helper function to solve the equation for Pi numerically and than put in the analytical solutions for all the other steady-state variables.

When I run this in Dynare it doesn’t complain about the steady-state and after running the resid command, it shows all residuals as zero. I therefore thought, that I made no mistake when calculating the solutions for the steady-state model. For any other value of Pi, except the solution of the numerical equation(I checked with mathematica and it only has 1 solution), Dynare tells me, that the steady-state file does not compute the steady-state.

In my understanding, this meant, that there is only a single solution for the steady-state of the model and it is not zero for the steady-state inflation. However, I later discovered, that when the author (from the paper above) did his log-linearizations, he used a zero-inflation steady-state and I wondered how this is possible, since the steady-state model has no solution for a steady-state inflation of zero.