Linking Dynare to Matlab code

Sorry to bump the thread again, but it’s somewhat related to the initial question.

After some time, I got the SMM working no problem – what is a slight issue, however, is that there are some moments I want to match that are long run growth rates of some variables. However, as you know better than anyone else, dynare focuses more on cyclical fluctuations. My initial understanding that long run growth was built in merely by doing:

z_t = rho*z_t-1 + (1-rho)*growth + eps

where growth = .03, for example. However, taking the average across the variables is still zero (over the simulated series). I looked for previous threads on this and the only related one, I think, was [Growth of variables and unit root), however, it didn’t have a response.

One way to deal with this, of course, is to “add in” the long run growth component afterwards, but that would change the dynamic choices I’d think. Is there a simple way to do this I’m overlooking? Note that the issue isn’t solved by detrending since I want the model to be able to produce some long run growth.