Currently I am woking on a DSGE model using Dynare and want to compare its moments with real data. Real data usually expressed in logs and HPfiltered. To obtain log deviations (percentage deviations) for variables in my model, one way is to make exp() trasformation for each variable.
I was wondering whether adding extra variables, like logY logC and adding new equations logY=log(Y), would also provide me log deviations for those extra variables? So are these two ways equivalent?
Plus should I expect different IRF behaviors between a nonlinear model and exp() transformed model?
I appreciate your help