I am writing for the following question.
While using Dynare I have noticed that working with log-linearized equations (e.g the log-linearization is operated by hand by myself) rather than Non-linear exp() equations (e.g. the log-linearization is operated by Dynare) seems to have an impact on Theoretical moments as well as Policy Functions Coefficients.
In particular, it seems to me that differences in variables standard deviations may reach the 9-10% (even tough on average their magnitude is smaller, like 2-3%). I attach below a minimal model code which shows this point (RBC1 is log-linear, RBC is exp() Non-linear).
Now, my interpretation is that this is because Dynare performs the derivatives numerically and therefore delivers slightly different results due to the underlying approximation. Then my questions are:
Is my interpretation correct?
If that is the case, how can we discern differences due by errors in the log-linear model derivation (e.g errors in the log-linearizations by hand) from differences due by Dynare approximation? E.g Which is the magnitude of differences in thereotical std (or policy function coefficients) which one should naturally expect and what is instead a “too big” difference?
A remark: if you are wondering why I am interested, consider that while dealing with large scale DSGE models it may be useful to compare the outcomes of the two codes (Non-linear model vs log-linear) as an extra double check.
Thank you in advance,