Dear all and Professor Pfeifer,

I have a question about the DSGE modeling and its stochastic simulation results.

I have the following equation:

I thought the equation holds and therefore the IRFs of its difference should be zero at all horizons then, but it seems not. At t=0, when the shock hits, the equation does not hold as shown in the figure below:

In the figure, if we shift all the time scripts one period back, at time t=0, the IRF of the Gamma(-1) term is zero as expected. However, the IRF of diff (the LHS minus the RHS) is not zero at time t=0. The IRFs of diff is zero when t>=1, which means the equation holds only when t>=1. So why it does not hold at time t=0? And at time t=0, since the equation does not hold, how are the LHS and Omega_ratio term determiend then?

I would really appreciate that if anyone could help!

Thanks so much!

Best,

Bob