As I understand, it is usually common practice, to choose DSGE models in such a way, that the steady-state inflation is freely choose-able and for simplifications it is than usually assumed to be zero.

My question is now, how is this usually achieved?

For a while now, I have been trying to replicate this paper. It appears to me, that the author does exactly that, he assumes a steady-state inflation of zero and log-linearizes the model around it. However, when I try to confirm this and solve the steady-state calculations, the model does not appear to have a freely choose-able steady-state inflation and in fact, it is different from zero. When I solve the steady-state for this model, I unsurprisingly get 12 equations and 12 variables and the model solves exactly. I assume this happens quite often, is there a trick to achieve a undetermined steady-state inflation?

As a second question, in the model above, the author did not specify the monetary policy in the beginning, but when he later summarized his log-linearized equations, he specified a simple taylor rule, of the form: \begin{align} \hat{R_t} = \phi_\Pi \hat{\pi_t} + \phi_y \hat{Y_t} \end{align} In order to calculate the steady-state of the model (before the log-linearizations), I assumed the nonlinear monetary policy equation to be: \begin{align} R_t = \Pi_t^{\phi_\pi} * Y_t^{\phi_y} \end{align} This made sense to me, since when log-linearizing this equation it becomes the equation specified by the author and I therefore thought, that it is the correct nonlinear counterpart of the monetary policy equation. But now I think this assumption may be my mistake and is why in my steady-state calculations, the inflation can not be zero.

In case someone ever has the same issue. I understand my problem now. When doing the backwards log-linearization, I already divided by the steady_state equation. But actually I shouldn't have done that. The nonlinear Taylor-Rule should look like this: \begin{align} \frac{R_t}{\bar{R}} = \bigg(\frac{\Pi_t}{\bar{\Pi}}\bigg)^{\phi_\pi} * \bigg(\frac{Y_t}{\bar{Y}}\bigg)^{\phi_y} \end{align} This way, the equation cancels in the steady-state and I can freely choose a steady-state inflation, as long as it is consistent with the real rate determined by preferences. This was not possible before, since the nominal rate was fixed by this equation.