I've combined this calculation (solving for NGDP by integrating a differential equation) with this finding (that the nominal shocks in the DSGE form of the model are approximately given by shocks to employment) -- the latter meaning that the the noise function n(t) is given by changes in employment.
The result is fairly good (for such a simple model) over short periods (the validity of the DSGE form). In the graphs: the IT model is blue, the IT model using empirical shocks is red (this should recover the original data -- errors are numerical), and the NGDP data is black.
One thing to note is that the employment shocks result in a much smoother transition to recession. That's because employment is much smoother than NGDP.