# What is the difference between the pulse diagram of stochastic simulation and that of perfect foresight simulation? **URL:** \ **Category:** Stochastic simulations\ **Created:** [24 October 2023 07:06 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008 "2023-10-24T07:06:44Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![wenzhuo](https://forum.dynare.org/letter_avatar_proxy/v4/letter/w/f9ae1b/32.png) [@wenzhuo](https://forum.dynare.org/u/wenzhuo)\ **Post date:** [24 October 2023 07:06 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008/1 "2023-10-24T07:06:44Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [24 October 2023 09:16 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008/2 "2023-10-24T09:16:28Z")
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. ---
**Author:** ![wenzhuo](https://forum.dynare.org/letter_avatar_proxy/v4/letter/w/f9ae1b/32.png) [@wenzhuo](https://forum.dynare.org/u/wenzhuo)\ **Post date:** [24 October 2023 12:04 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008/3 "2023-10-24T12:04:29Z")
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? ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [24 October 2023 12:27 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008/4 "2023-10-24T12:27:07Z")
Which exact reference do you have in mind. Please elaborate. ---
**Author:** ![wenzhuo](https://forum.dynare.org/letter_avatar_proxy/v4/letter/w/f9ae1b/32.png) [@wenzhuo](https://forum.dynare.org/u/wenzhuo)\ **Post date:** [24 October 2023 13:20 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008/5 "2023-10-24T13:20:30Z")
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? ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [26 October 2023 20:34 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008/6 "2023-10-26T20:34:27Z")
Have a look at > [@Stoch\_simull(order=1) and news shocks](https://forum.dynare.org/t/stoch-simull-order-1-and-news-shocks/6282): > > Dear all, I have a stupid and embarrassing question to ask. I let dynare solve my DSGE model by choosing a first order Taylor approximation (i.e. stoch\_simull(order=1,…) ). However, we know that 1st order linearizations yield the certainty equivalence property. Since my model contains news shocks, is there a conflict regarding the approximation number? As we know it is quite complicated to introduce news shocks into perfect foresight models. Many thanks in advance for your help. Best Robert ---
**Author:** ![wenzhuo](https://forum.dynare.org/letter_avatar_proxy/v4/letter/w/f9ae1b/32.png) [@wenzhuo](https://forum.dynare.org/u/wenzhuo)\ **Post date:** [29 October 2023 12:49 UTC](https://forum.dynare.org/t/what-is-the-difference-between-the-pulse-diagram-of-stochastic-simulation-and-that-of-perfect-foresight-simulation/24008/7 "2023-10-29T12:49:10Z")
Thanks a lot !