# Third order approximation and its discontents

**URL:** <https://forum.dynare.org/t/third-order-approximation-and-its-discontents/15592>\
**Category:** Stochastic simulations\
**Created:** [16 April 2020 14:22 UTC](https://forum.dynare.org/t/third-order-approximation-and-its-discontents/15592 "2020-04-16T14:22:23Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![IrfanQureshi](https://forum.dynare.org/letter_avatar_proxy/v4/letter/i/aeb1de/32.png) [@IrfanQureshi](https://forum.dynare.org/u/IrfanQureshi)\
**Post date:** [16 April 2020 14:22 UTC](https://forum.dynare.org/t/third-order-approximation-and-its-discontents/15592/1 "2020-04-16T14:22:23Z")

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Hi everyone,

I am using dynare 4.5.6. My key question is related to understanding the third order approximation of the type used in Basu & Bundick (2017), henceforth BB (2017) and generating IRFs.

Here is what I am doing:

I want to understand what happens to output when there is uncertainty about productivity. I take the standard RBC model (Listing 6). I include a lagged term in the productivity equation (similar to what is done in BB (2017) – they explain this on page 13 here: [https://fmwww.bc.edu/ec-p/wp774.pdf](https://fmwww.bc.edu/ec-p/wp774.pdf)).

I include a shock process for this term. I then add stoch\_simul(order=3,irf=20) because I want to extract the effect of uncertainty on output. Given the small size of the shocks my IRFs are well behaved.

I noticed, however, that there has been an active discussion on this forum ([Simult\_ and nonzero IRFs in higher-order approximations](https://forum.dynare.org/t/simult--and-nonzero-irfs-in-higher-order-approximations/4523/5))  
Also, the excellent BB (2017) replication and the Born/Pfeifer (2014): “Risk Matters: A comment” goes beyond the simple stoch\_simul to generate IRFs. My questions:

1. Do I need to use the simult\_ function to compute IRFs around the stochastic steady state?
2. I also noticed that when I change the irf = 20 to irf = 10, the second order IRF change. Why is that?

Attaching the code here.[RBC.mod](https://forum.dynare.org/uploads/short-url/kvAUwz5elhYeuy63V86UquMaDiZ.mod) (1.5 KB)

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**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:** [17 April 2020 08:48 UTC](https://forum.dynare.org/t/third-order-approximation-and-its-discontents/15592/2 "2020-04-17T08:48:24Z")

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1. Yes, you need to use the `simult_`-function to generate IRFs at the stochastic steady state. Using the standard Dynare `stoch_simul`-command will generate IRFs at the ergodic mean.
2. That implies that your IRFs have not yet converged to the ergodic distribution, i…e. you need to increase `replic`. Using a different IRF length results in different random numbers being drawn across the replications.