# Second order approximation and Shock sizes

**URL:** <https://forum.dynare.org/t/second-order-approximation-and-shock-sizes/28024>\
**Category:** Stochastic simulations\
**Created:** [10 October 2025 15:28 UTC](https://forum.dynare.org/t/second-order-approximation-and-shock-sizes/28024 "2025-10-10T15:28:14Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![lovefukanglin](https://forum.dynare.org/letter_avatar_proxy/v4/letter/l/8edcca/32.png) [@lovefukanglin](https://forum.dynare.org/u/lovefukanglin)\
**Post date:** [10 October 2025 15:28 UTC](https://forum.dynare.org/t/second-order-approximation-and-shock-sizes/28024/1 "2025-10-10T15:28:14Z")

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Dear, professor jpfeifer,

I simulate my model at first order, everything goes right and I get the corresponding IRFs.

The problem is the second order approximation for welfare analysis.

I find the means of variables are extremely huge if I use the shock sizes calibrated from literature.

If I reduce all the shock sizes by dividing by 100, the means of variables are similar with the first order.

Can I just reduce the shock sizes and use them in first order for IRFs and second order for welfare analysis? However, the shock sizes will differ with relevant literature.

I update the files and hope you can run it and give me some suggestions on why these happen; How to set the shock size and obtain welfare results at second order.

Thank you so much!

[finalcode202509.mod](https://forum.dynare.org/uploads/short-url/46sJgsZ6OF36buRSmtDOIRCzsbH.mod) (23.9 KB)

[finalcode202509calib.m](https://forum.dynare.org/uploads/short-url/rjSwkcnCOUWeTFZgAXu6aLSswZG.m) (5.6 KB)

[finalcode202509\_steady.m](https://forum.dynare.org/uploads/short-url/xDrmZZKTLkJZh9uKNphWLx38JLE.m) (4.6 KB)

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<div class="post-metadata">

**Author:** ![lovefukanglin](https://forum.dynare.org/letter_avatar_proxy/v4/letter/l/8edcca/32.png) [@lovefukanglin](https://forum.dynare.org/u/lovefukanglin)\
**Post date:** [14 October 2025 11:07 UTC](https://forum.dynare.org/t/second-order-approximation-and-shock-sizes/28024/2 "2025-10-14T11:07:25Z")

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Dear professor jpfeifer, I still can not **handle this problem. Hope you can give me some suggetions when you have time. Thank you so much.**

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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:** [15 October 2025 08:08 UTC](https://forum.dynare.org/t/second-order-approximation-and-shock-sizes/28024/3 "2025-10-15T08:08:48Z")

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Your model looks overly volatile to me. If I use

```auto
stoch_simul(order=1,irf=0,replic=1000,irf_shocks=(e_Df2,e_Xh, e_M)) Ci Hi;

```

I get

```auto
THEORETICAL MOMENTS
VARIABLE MEAN STD. DEV. VARIANCE
Ci 0.4747 0.4422 0.1955
Hi 0.1873 0.4094 0.1676

```

which is a fourty percent standard deviation of consumption! That is huge and explains the welfare results. You need to understand why the model produces behavior like that.

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<div class="post-metadata">

**Author:** ![lovefukanglin](https://forum.dynare.org/letter_avatar_proxy/v4/letter/l/8edcca/32.png) [@lovefukanglin](https://forum.dynare.org/u/lovefukanglin)\
**Post date:** [15 October 2025 14:27 UTC](https://forum.dynare.org/t/second-order-approximation-and-shock-sizes/28024/4 "2025-10-15T14:27:50Z")

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Yes, you are right, professor.

I check all the variables and find 5-6 variables have huge standard deviations.

I will rethink and modify the model and parametrization parts.

Always thank you for your times and substantial helps.

Thank you so much!