Using empirical estimates (from %-deviation) for simulation

[jpfeifer]

I am not completely following what you are doing here. When you define

y = y_bar*exp(yhat) 

then yhat measures percentage deviations from y_bar. See [Comparing model with data after log-linearization) on how to compare model and data moments

What you need to get straight is the filtering issue. You are not supposed to estimate AR1-processes on HP-filtered data. What you seem to be aiming for is a moment matching.

Regarding

I tried defining a logged version of y to see what would happen, but noticed that the IRF for the logged version looked no different than the IRF for the non-logged version, in terms of both shape and scale (but again…I’ve been working for a while and perhaps am not thinking clearly here).

The IRF to the logged version is the IRF to the unlogged version divided by the steady state (Jacobian transformation). Thus, if your steady state is close to 1 they will be (almost) the same.