Different utility function, same investment shock output

[dynaregeek]

I have two .mod files:

• The first one with a non separable utility function
• The second one with a separable utility function
  The model is a Neokeynesian with nominal frictions.
  Using the same parameters and different utility function, I get the same results in the plots.
  Is this possible and normal? Is it a problem of scale?
  esercizio1.mod (4.2 KB)
  esercizio2.mod (4.1 KB)

[jpfeifer]

That depends on the particular utility functions and the approximation order. When performing a first order approximation, separability might be re-introduced.

[dynaregeek]

I have on the first .mod file

And on the second .mod file “esercizio2.mod”

Using the same constraints for firms and households, same Taylor rule, same law of motion of capital by reintroducing separability with approximation (log linearization)
what happens to the steady state? It remains the same for each model?
Is the shock output equal because of the same steady state parameters?

[jpfeifer]

With sigma=1 as in your model you are considering the log case, which makes the two identical.