# Shocks and steady state

**URL:** <https://forum.dynare.org/t/shocks-and-steady-state/19174>\
**Category:** General DSGE Modeling\
**Created:** [25 October 2021 11:03 UTC](https://forum.dynare.org/t/shocks-and-steady-state/19174 "2021-10-25T11:03:41Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![michaelm](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/3be4f8/32.png) [@michaelm](https://forum.dynare.org/u/michaelm)\
**Post date:** [25 October 2021 11:03 UTC](https://forum.dynare.org/t/shocks-and-steady-state/19174/1 "2021-10-25T11:03:41Z")

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Hi  
I am a novice and I have reached a contradiction. please correct my mistake. Thanks in advance  
Productivity comes in two forms in the models(As far as I have seen):

![image](https://forum.dynare.org/uploads/default/original/2X/9/9efe578169d5585c64e31fe5de2ccdbd05fb8ec2.png)  
Of course, I know these two are one, but the models use one of these two forms

Now when we want to calibrate the steady state:

According to the first method:

Log(A)=rho\_A\*log(A) Therefore A=1

According to the second method: A=1

Now my question is about the other shocks. For example, shock to government spending in the RBC model([DSGE\_mod/RBC\_baseline.mod at master · JohannesPfeifer/DSGE\_mod · GitHub](https://github.com/JohannesPfeifer/DSGE_mod/blob/master/RBC_baseline/RBC_baseline.mod))  
If we use the following form:

![image](https://forum.dynare.org/uploads/default/original/2X/e/e421d8953b0f55e0e8146544a13ceaa26731f24a.png)

g\_ss=g and g=gshare\*y;  
That is, g\_ss is not necessarily equal to 1. It depends on gshare  
That is reasonable

But if we use the second form:  
 ![image](https://forum.dynare.org/uploads/default/original/2X/2/2426242bf2145770d3ab35336638de32dcfbca01.png)  
In the steady state:  
Log(g)=rho\_g\*log(g) Therefore g=1

That is, in other equations, if we have g, we put it equal to 1(in steady state).  
What is my mistake??

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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:** [25 October 2021 11:49 UTC](https://forum.dynare.org/t/shocks-and-steady-state/19174/2 "2021-10-25T11:49:44Z")

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It should be  
\log g\_t=(1-\rho\_g)\log g^\*+\rho\_g \log g\_{t-1}+\varepsilon\_t^G

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**Author:** ![HelloDynare](https://forum.dynare.org/user_avatar/forum.dynare.org/hellodynare/32/12107_2.png) [@HelloDynare](https://forum.dynare.org/u/HelloDynare)\
**Post date:** [25 October 2021 12:28 UTC](https://forum.dynare.org/t/shocks-and-steady-state/19174/3 "2021-10-25T12:28:14Z")

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Hi @michaelm, I’m also a novice 🙂  
As a cross-reference, You may also have a look at:

> [@How to log-linearize different forms of technology shocks?](https://forum.dynare.org/t/how-to-log-linearize-different-forms-of-technology-shocks/11106):
>
> Hello everyone, there are some question I would like to ask for your help. When I read paper, I find there are mainly two forms of shocks, take the technoloty shock as an example: One kind of the forms is (1):[1] , and for this form, the corresponding log-linearization is[2] , and the steady state value of technology shock is [3] when in equilibrium. The other form of technology shock is (2):[4] , for this form, I don’t know how to log-linearize the technology shock, is the same as the first …