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Hello! I have a rather general question (probably also a naive one) about Bayesian estimation of DSGE models.
Usually people calibrate the parameters that affect the steady-state and estimate those that affect the dynamics of the model.

Is it possible to estimate ALL model parameters with Bayesian methods?

Any help would be very much apperciated (also links to related literature)

Yes, it is possible to estimate those parameters, but you have to make sure they are identified. That often means that you need e.g. leave the constant part of the observation equation in there, i.e. one should not use demeaned first differences. Examples of such models are Smets/Wouters (2007) and Fernandez-Villaverde's "Econometrics of DSGE models".