Are log-linearization and calculation of Hessian matrix involved in this DSGE model

Dear Johannes,
Thank you very much your previous help, I am grateful.
I am following this paper ‘Risk Shocks’(Attachment
CMR.pdf (1.2 MB)
) to develop new DSGE models for my research question, however, I think it is a nonlinear DSGE model right? Does estimation for any nonlinear DSGE model involve log-linearization and calculation of Hessian matrix to identify parameters?
Thank you very much and look forward to hearing from you.
Best regards,

You are confusing things. The CMR model is a nonlinear model solved linearly. You could also estimate nonlinear models e.g. using particle filters or GMM. The Hessian at the mode is only computed to generate a proposal density for the MCMC, but that is not a necessary step. Pretty much any positive definite matrix should work. But this has nothing to do with identification.