Log-linearization vs variables in logs

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


How are the variables expressed in your model?

variables are expressed as in nonlinear equations. For example euler equation is beta*(1+r)(1/c(+1))=(1/c)(1+eta*b). I also find the SS for nonlinear model. But then to compare with the real log hp filtered data, I define additional variables and express lnc=logĀ©, so I look at the moments of these additional variables.

I was wondering whether this is a appropriate process?