# Estimation of third order approximation

**URL:** <https://forum.dynare.org/t/estimation-of-third-order-approximation/4252>\
**Category:** SMM/GMM/IRF-Matching\
**Created:** [29 October 2014 06:54 UTC](https://forum.dynare.org/t/estimation-of-third-order-approximation/4252 "2014-10-29T06:54:03Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![alexmaci](https://forum.dynare.org/letter_avatar_proxy/v4/letter/a/7c8e57/32.png) [@alexmaci](https://forum.dynare.org/u/alexmaci)\
**Post date:** [29 October 2014 06:54 UTC](https://forum.dynare.org/t/estimation-of-third-order-approximation/4252/1 "2014-10-29T06:54:03Z")

</div>

Hi  
I just wanted to ask if dynare is able to estimate (and also make a historical decomposition of shocks) a model which has a third-order approximation ? This third order is needed to generate time variant term premia of financial assets.  
Many Thanks

---

<div class="post-metadata">

**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:** [29 October 2014 09:43 UTC](https://forum.dynare.org/t/estimation-of-third-order-approximation/4252/2 "2014-10-29T09:43:57Z")

</div>

No, that is not possible with Dynare. The particle filter currently is still experimental and does not yet support third order. Note that shock decompositions (in the sense of contributions of shocks to particular variables) at higher order are non-trivial due to non-linearity. There is no agreed upon standard way of doing this. If you only want to extract shocks, a particle smoother could work.  
You could aslo try to estimate your model using GMM or SMM. An SMM example is contained in our replication files for Born/Pfeifer (2014): “Risk Matters: A comment” on my homepage.

---

<div class="post-metadata">

**Author:** ![zhanghuifd](https://forum.dynare.org/letter_avatar_proxy/v4/letter/z/ebca7d/32.png) [@zhanghuifd](https://forum.dynare.org/u/zhanghuifd)\
**Post date:** [28 November 2017 11:34 UTC](https://forum.dynare.org/t/estimation-of-third-order-approximation/4252/3 "2017-11-28T11:34:57Z")

</div>

Hi, if there any reference besides FGRU and BP2014 is related to estimation of DSGE model at third order?

Thanks !

---

<div class="post-metadata">

**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:** [1 December 2017 06:51 UTC](https://forum.dynare.org/t/estimation-of-third-order-approximation/4252/4 "2017-12-01T06:51:24Z")

</div>

What are you looking for?

---

<div class="post-metadata">

**Author:** ![zhanghuifd](https://forum.dynare.org/letter_avatar_proxy/v4/letter/z/ebca7d/32.png) [@zhanghuifd](https://forum.dynare.org/u/zhanghuifd)\
**Post date:** [2 December 2017 05:32 UTC](https://forum.dynare.org/t/estimation-of-third-order-approximation/4252/5 "2017-12-02T05:32:27Z")

</div>

Hi, professor! I want to estimate a simple RBC model at third order approximation by method of GMM/SMM. But I think it is a bit hard for me. Is there any material for a beginner to grasp the method of GMM/SMM at third order approximation?

I tried to apply your method in BP2014. But I am not sure what any modification is required.  
Thanks!

---

<div class="post-metadata">

**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:** [8 December 2017 09:56 UTC](https://forum.dynare.org/t/estimation-of-third-order-approximation/4252/6 "2017-12-08T09:56:56Z")

</div>

If your model is just identified, i.e. you estimate as many parameters as you match moments, then the changes you need to do are minimal. What are you unsure about?