Different forms of Shocks

General DSGE Modeling
1

Hi everyone,

I have a basic question regarding the types of shockes we can use in a DSGE model. For example in one type, there is an AR(1) process without any intercept or other terms:

ln(AT)=rhoat*ln(AT(-1))+EPS_AT;

In another type, we include the steady state of the variable into the shock formula:

ln(AT)=rho*ln(AT(-1))+(1-rho)*ln(steady_state(AT))+EPS_RHO;

Sometimes, the steady state of a variable is 1 and the second type changes the first one but what if the steady state is different than 1? Does using different forms depend on whether the model is written in a nonlinear form?

2

The first formulation hard-codes the steady state to be 1. The second one allows to set the steady state to any arbitrary value. Both versions would not appear in a linear model due to the use of log.

3

Thanks a lot. I always appreciate your help.
If the second one is more general, what is the reason of using the first formolation for many researchers? I am wondering that they can easily use the second one and set the steady state value to 1 to get the first one.

4

For many processes, the natural steady state is 1. Why go for something more complicated, if the easy one suffices?

5

Thanks again for your help.
Correct. It makes sense.
Just a quick question, could you provide me with some processes which their natural steady states are 1. I’ve seen that for the technolody shock, what about other examples?

6

Pretty much any shocks that enters multiplicatively. Examples are TFP shocks or monetary policy shocks.

7

Thank you so much!