# What is the difference between the pulse diagram of stochastic simulation and that of perfect foresight simulation?

Hi,
I am learning the stoch_simul command of DSGE, but when I saw the pulse diagram, I suddenly couldn’t tell the difference between the pulse diagram of this kind and the pulse diagram of the perfect foresight model. It seems to me that the result is the same. Could anyone help me to answer it?
Thanks a lot

At first order, you have certainty equivalence. If you only consider surprise shocks and the model is linear, you will get exactly the same IRFs.

Many thanks for your kind reply, which really helps me a lot. Could I ask a further question? If I consider the expected shock, using the perfect foresight model for the expected shock, and referring to the method of Milani (2011) for the expected shock in the stochastic simulation, will the pulse diagram of the two be the same?

Which exact reference do you have in mind. Please elaborate.

The examples I may give are not appropriate, because I am not familiar with them yet.
For example, there is white noise epsi in the taylor rule. In the perfect foresight model, the expected shock can be set to occur in the third period in the future. When carrying on the expected shock in the stochastic model, according to the method of Milani (2011), we introduce the equation “At=epsi(0,t)+epsi(1,t-1)+epsi(2,t-2)”. Will the pulses obtained by the above two methods be the same?

Have a look at

Thanks a lot !